References - link.springer.com3A978-1... · References Abe,M.,2009, VehicleHandlingDynamics:TheoryandApplication ,Butterworth-Heinemann, Oxford, UK. Alkhatib, R., Jazar, R. N., and

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Tra c Accidents, Sixth Edition, National Safety Council, Itasca, Illinois,1996.Andrzejewski, R., and Awrejcewicz, J., 2005, Nonlinear Dynamics of a

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Wiley & Sons, New York.Balachandran, B., Magrab, E. B., 2003, Vibrations, Brooks/Cole, Paci c

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The Geometry of Motion, Plenum Press, New York.Benaroya, H., 2004,Mechaniscal Vibration: Analysis, Uncertainities, and

Control, Marcel Dekker, New York.Bourmistrova, A., Simic, M., Hoseinnezhad, R., and Jazar, Reza N., 2011,

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Vehicles, Journal of Vibration and Control, 16(2), 253-279.Jazar, Reza. N., 2011, Advanced Dynamics: Rigid Body, Multibody, and

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References1030

Appendix A

Frequency Response CurvesThere are four types of -DOF harmonically excited systems as shownin Figure 12.39:

1 base excitation,2 eccentric excitation,3 eccentric base excitation,4 forced excitation.

The frequency responses of the four systemscan be summarized, labeledand shown as follows:

0 = (A.1)

=1q

(1 2)2+ (2 )

2(A.2)

1 = (A.3)

= q(1 2)

2+ (2 )

2(A.4)

2 =¨

= = = (A.5)

=2q

(1 2)2+ (2 )

2(A.6)

3 = = = (A.7)

=3q

(1 2)2+ (2 )

2(A.8)

4 =¨

2=

¨

2=

¨

2(A.9)

=4q

(1 2)2+ (2 )

2(A.10)


1031

1032 Appendix A. Frequency Response Curves

r

0S

0

0.1

0.2

0.3

0.4

0.50.6

0.81.0

/F

0XSF k

FIGURE A.1. Frequency response for 0.

0 = = (A.11)

=

q1 + (2 )

2q(1 2)

2+ (2 )

2(A.12)

1 = (A.13)

=

q1 + (2 )

2q(1 2)

2+ (2 )

2(A.14)

2 =¨

2= =

2=

2

³1 +

´(A.15)

=

2

q1 + (2 )

2q(1 2)

2+ (2 )

2(A.16)

Appendix A. Frequency Response Curves 1033

r

1S

0

0.1

0.2

0.3

0.4

0.50.6

0.81.0

/F

1XS

F km


r

2S

0

0.2

0.1

0.3

0.40.5

0.6

0.81.0

/F B E R

2E R

X Z X ZSF m Y e e



r

3S

00.1

0.3

0.4

0.5

0.6

0.81.0

0.2

B E R3

n E n R n

Z X ZSY e e


r

4S

0

0.1

0.3

0.4

0.5

0.60.8

1.0

0.2

B E R4 2 2 2

n E n R n

Z X ZSY e e


Appendix A. Frequency Response Curves 1035

r

0G

00.1

0.3

0.50.60.8

1.0

0.2

0.4

FT B0

F XGF Y


r

1G

0

0.1

0.3

0.50.6

0.81.0

0.2

0.4

B1

n

XGY



r

2G

0

0.1

0.3

0.50.60.81.0

0.2

0.4

E E RT T TB a2 2 2 2

n n e n e

F F FX mG 1kY mY e m e m


Appendix B

Trigonometric FormulasDe nitions in Terms of Exponentials

cos =+

2(B.1)

sin =2

(B.2)

tan =( + )

(B.3)

= cos + sin (B.4)

= cos sin (B.5)

Angle Sum and Di erence

sin( ± ) = sin cos ± cos sin (B.6)

cos( ± ) = cos cos sin sin (B.7)

tan( ± ) =tan ± tan1 tan tan

(B.8)

cot( ± ) =cot cot 1

cot ± cot (B.9)

Symmetry

sin( ) = sin (B.10)

cos( ) = cos (B.11)

tan( ) = tan (B.12)

Multiple Angles

sin(2 ) = 2 sin cos =2 tan

1 + tan2(B.13)

cos(2 ) = 2 cos2 1 = 1 2 sin2 = cos2 sin2 (B.14)

tan(2 ) =2 tan

1 tan2(B.15)


1037

1038 Appendix B. Trigonometric Formulas

cot(2 ) =cot2 1

2 cot(B.16)

sin(3 ) = 4 sin3 + 3 sin (B.17)

cos(3 ) = 4 cos3 3 cos (B.18)

tan(3 ) =tan3 + 3 tan

3 tan2 + 1(B.19)

sin(4 ) = 8 sin3 cos + 4 sin cos (B.20)

cos(4 ) = 8 cos4 8 cos2 + 1 (B.21)

tan(4 ) =4 tan3 + 4 tan

tan4 6 tan2 + 1(B.22)

sin(5 ) = 16 sin5 20 sin3 + 5 sin (B.23)

cos(5 ) = 16 cos5 20 cos3 + 5 cos (B.24)

sin( ) = 2 sin(( 1) ) cos sin(( 2) ) (B.25)

cos( ) = 2 cos(( 1) ) cos cos(( 2) ) (B.26)

tan( ) =tan(( 1) ) + tan

1 tan(( 1) ) tan(B.27)

Half Angle

cos³2

´= ±

r1 + cos

2(B.28)

sin³2

´= ±

r1 cos

2(B.29)

tan³2

´=1 cos

sin=

sin

1 + cos= ±

r1 cos

1 + cos(B.30)

sin =2 tan 2

1 + tan2 2

(B.31)

cos =1 tan2 2

1 + tan2 2

(B.32)

Powers of Functions

sin2 =1

2(1 cos(2 )) (B.33)

sin cos =1

2sin(2 ) (B.34)

cos2 =1

2(1 + cos(2 )) (B.35)

Appendix B. Trigonometric Formulas 1039

sin3 =1

4(3 sin( ) sin(3 )) (B.36)

sin2 cos =1

4(cos 3 cos(3 )) (B.37)

sin cos2 =1

4(sin + sin(3 )) (B.38)

cos3 =1

4(cos(3 ) + 3 cos )) (B.39)

sin4 =1

8(3 4 cos(2 ) + cos(4 )) (B.40)

sin3 cos =1

8(2 sin(2 ) sin(4 )) (B.41)

sin2 cos2 =1

8(1 cos(4 )) (B.42)

sin cos3 =1

8(2 sin(2 ) + sin(4 )) (B.43)

cos4 =1

8(3 + 4 cos(2 ) + cos(4 )) (B.44)

sin5 =1

16(10 sin 5 sin(3 ) + sin(5 )) (B.45)

sin4 cos =1

16(2 cos 3 cos(3 ) + cos(5 )) (B.46)

sin3 cos2 =1

16(2 sin + sin(3 ) sin(5 )) (B.47)

sin2 cos3 =1

16(2 cos 3 cos(3 ) 5 cos(5 )) (B.48)

sin cos4 =1

16(2 sin + 3 sin(3 ) + sin(5 )) (B.49)

cos5 =1

16(10 cos + 5 cos(3 ) + cos(5 )) (B.50)

tan2 =1 cos(2 )

1 + cos(2 )(B.51)

Products of sin and cos

cos cos =1

2cos( ) +

1

2cos( + ) (B.52)

sin sin =1

2cos( )

1

2cos( + ) (B.53)

sin cos =1

2sin( ) +

1

2sin( + ) (B.54)

1040 Appendix B. Trigonometric Formulas

cos sin =1

2sin( + )

1

2sin( ) (B.55)

sin( + ) sin( ) = cos2 cos2 = sin2 sin2 (B.56)

cos( + ) cos( ) = cos2 + sin2 (B.57)

Sum of Functions

sin ± sin = 2 sin±2

cos±2

(B.58)

cos + cos = 2 cos+

2cos

2(B.59)

cos cos = 2 sin+

2sin

2(B.60)

tan ± tan =sin( ± )

cos cos(B.61)

cot ± cot =sin( ± )

sin sin(B.62)

sin + sin

sin sin=tan +

2

tan +2

(B.63)

sin + sin

cos cos= cot

+

2(B.64)

sin + sin

cos + cos= tan

+

2(B.65)

sin sin

cos + cos= tan

2(B.66)

Trigonometric Relations

sin2 sin2 = sin( + ) sin( ) (B.67)

cos2 cos2 = sin( + ) sin( ) (B.68)

Appendix C

Unit ConversionsGeneral Conversion Formulas

N m s 4 448 × 0 3048 × lb ft s

4 448 × 0 0254 × lb in s

lb ft s 0 2248 × 3 2808 × N m s

lb in s 0 2248 × 39 37 × N m s

Conversion FactorsAcceleration

1 ft s2 0 3048m s2 1m s2 3 2808 ft s2

Angle1 deg 0 01745 rad 1 rad 57 307 deg

Area1 in2 6 4516 cm2 1 cm2 0 155 in2

1 ft2 0 09290304m2 1m2 10 764 ft2

1 acre 4046 86m2 1m2 2 471× 10 4 acre

1 acre 0 4047 hectare 1 hectare 2 471 acre

Damping

1N s m 6 85218× 10 2 lb s ft 1 lb s ft 14 594N s m

1N s m 5 71015× 10 3 lb s in 1 lb s in 175 13N s m

Energy and Heat

1Btu 1055 056 J 1 J 9 4782× 10 4Btu

1 cal 4 1868 J 1 J 0 23885 cal

1 kWh 3600 kJ 1MJ 0 27778 kWh

1 ft lbf 1 355818 J 1 J 0 737562 ft lbf


1041

1042 Appendix C. Unit Conversions

Force1 lb 4 448222N 1N 0 22481 lb

Fuel Consumption

1 l 100 km 235 214583mi gal 1mi gal 235 214583 l 100 km

1 l 100 km = 100 km l 1 km l = 100 l 100 km

1mi gal 0 425144 km l 1 km l 2 352146mi gal

Length

1 in 25 4mm 1 cm 0 3937 in

1 ft 30 48 cm 1m 3 28084 ft

1mi 1 609347 km 1km 0 62137mi

Mass1 lb 0 45359 kg 1 kg 2 204623 lb

1 slug 14 5939 kg 1 kg 0 068522 slug

1 slug 32 174 lb 1 lb 0 03 1081 slug

Moment and Torque

1 lb ft 1 35582Nm 1Nm 0 73746 lb ft

1 lb in 8 85075Nm 1Nm 0 11298 lb in

Mass Moment

1 lb ft2 0 04214 kgm2 1 kgm2 23 73 lb ft2

Power1Btu h 0 2930711W 1W 3 4121Btu h

1 hp 745 6999W 1kW 1 341 hp

1 hp 550 lb ft s 1 lb ft s 1 8182× 10 3 hp

1 lb ft h 3 76616× 10 4W 1W 2655 2 lb ft h

1 lb ft min 2 2597× 10 2W 1W 44 254 lb ft min

Pressure and Stress

1 lb in2 6894 757Pa 1MPa 145 04 lb in2

1 lb ft2 47 88Pa 1Pa 2 0886× 10 2 lb ft2

1Pa 0 00001 atm 1atm 101325Pa

Appendix C. Unit Conversions 1043

Sti ness

1N m 6 85218× 10 2 lb ft 1 lb ft 14 594N m

1N m 5 71015× 10 3 lb in 1 lb in 175 13N m

TemperatureC = ( F 32) 1 8

F = 1 8 C + 32

Velocity

1mi h 1 60934 km h 1 km h 0 62137mi h

1mi h 0 44704m s 1m s 2 2369mi h

1 ft s 0 3048m s 1m s 3 2808 ft s

1 ft min 5 08× 10 3m s 1m s 196 85 ft min

Volume

1 in3 16 39 cm3 1 cm3 0 0061013 in3

1 ft3 0 02831685m3 1m3 35 315 ft3

1 gal 3 785 l 1 l 0 2642 gal

1 gal 3785 41 cm3 1 l 1000 cm3

Index2R planar manipulator

dynamics, 611equations of motion, 613ideal, 611joint 2 acceleration, 294kinetic energy, 612Lagrangean, 612potential energy, 612

4-bar linkages, 317—319, 331, 332,336, 362

acceleration analysis, 324, 325concave, 322convex, 322coupler angle, 318coupler link, 318coupler point, 362—364coupler point curve, 362—366,

368, 369crank-crank, 326crank-rocker, 326crossed, 322dead positions, 327designing, 328drag-link, 326elbow-down, 322elbow-up, 322Grasho criterion, 326input angle, 318input link, 318input variable, 318limit positions, 326non-crossed, 322output angle, 318output link, 318position analysis, 318possible con gurations, 322rocker-rocker, 326spatial, 369

sweep angles, 331velocity analysis, 323

ABS, 75Acceleration, 197

angular, 287, 291—293, 295body point, 280, 294, 295, 573capacity, 196centripetal, 293Coriolis, 575matrix, 288tangential, 293tilting, 73

Accelerationpower-limited, 197traction-limited, 197

Acceleration capacity, 196Ackerman

condition, 385history, 401mechanism, 461

Ackermangeometry, 387mechanism, 387steering, 385, 387

Ackerman condition, 385Ackerman, Rudolf, 401Alfred Cornu, 435Aligning moment, 148, 150Angle

attitude, 244bank, 244camber, 100heading, 244inclination, 47, 63pitch, 244roll, 244sideslip, 100


1045

1046

spin, 244steering, 386tilting, 47, 49tire contact, 109tireprint, 109ultimate, 47, 48yaw, 244

Angular acceleration, 287, 288, 293,295

combination, 291in terms of Euler parameters,

292matrix, 288relative, 292vector, 288

Angular momentum, 580—584, 588,590

2 link manipulator, 587Angular velocity, 249—251, 267, 272

alternative de nition, 280, 282alternative proof, 282combination, 272, 291coordinate transformation, 274decomposition, 271Euler frequency, 249instantaneous, 268instantaneous axis, 269matrix, 267, 273principal matrix, 270transformation, 272vector, 249, 267

Arc length, 448Arthur Talbot, 436Atan2 function, 65Attitude angle, 631, 634Axis-angle rotation, 260, 262—264

B-derivative, 275Based excitation, 819

acceleration, 826, 828frequency response, 819transmitted force, 829velocity, 826, 828

Bernoulli, Jacques, 436Bicycle car

mode shape, 914, 915Natural frequency, 914, 915vibration, 911—914

Bicycle model, 647, 657, 665, 668,693, 755

body force components, 647camber trust, 763characteristic equation, 703coe cient matrix, 697, 756constant lateral force, 688control variables, 660, 664, 756,

758coordinate frame, 629, 630critical speed, 686curvature response, 668, 692,

695, 759eigenvalue, 703equations of motion, 755, 756force system coe cients, 652,

670, 754free dynamics, 764free response, 699, 705, 764global sideslip angle, 650hatchback, notchback, station,

775input vector, 660, 664, 758kinematic steering, 652lateral acceleration response,

668, 669, 680, 692, 695,759

linearized model, 693neutral distance, 687neutral steer, 684neutral steer point, 687Newton-Euler equations, 658oversteer, 684passing maneuver, 768, 771roll angle response, 760roll damping, 752roll steer, 763roll sti ness, 752rotation center, 711sideslip coe cient, 648, 750sideslip response, 668, 692slip response, 759

Index

1047

stability factor, 684steady state conditions, 695steady-state motion, 759steady-state response, 671, 687,

688, 759step input, 698, 706, 708, 766time response, 696, 763time series, 705torque coe cient, 752transient response, 697understeer, 684vehicle velocity vector, 650yaw rate response, 668, 692,

759zero steer angle, 699

Brake forcebalance, 75optimal, 75

Bump steering, 413

Camber, 528angle, 100, 158, 160, 521force, 158line, 552moment, 160sti ness, 159theory, 552torque, 160trail, 160trust, 158variation, 519

Camber angle, 521Camber theory, 552Car

classi cations, 26ying, 83

Cartesianangular velocity, 250

Caster, 527negative, 527positive, 527theory, 542

Caster angle, 527Caster theory, 542Catapults, 618

Centrifugal moments, 591Centripetal acceleration response,

668, 692Centro, 350Cesàro, Ernesto, 436Characteristic equation, 849Chasles theorem, 296, 307Christo el operator, 608Circumferential slip, 141Clothoid, 432

arc length, 432curvature, 433gure 8, 449, 453history, 435radius, 433road, 432scaling parameter, 432sharpness, 435tangent angle, 433

Clutch, 196dynamics, 192Foettinger, 196hydrodynamic, 196

Coordinate framebody, 631global, 631rim, 538tire, 533, 644vehicle, 533, 629, 631, 644,

737wheel, 533, 644wheel , 643wheel-body, 533, 643, 644

Coriolisacceleration, 291, 295e ect, 575force, 574

Cornering sti ness, 148Cornu spiral, 436Cornu, Alfred, 435Couple, 568, 570Coupler point curve, 362Cresting, 81Critical speed, 686Critically-damped

Index

1048

vibration, 853, 854Crouse angle, 631, 634Cruise angle, 634Curvature response, 668, 692, 695,

759Cycloid, 538, 539

curtate, 539prolate, 539

Damper, 793linear, 794parallel, 796, 797serial, 795viscous, 794

Damping ratio, 810determination, 860

De Dion suspension, 504Deviation moments, 591Di erential geometry

space curve, 448Di erentiating, 275

B-derivative, 275, 277G-derivative, 275, 280second, 282transformation formula, 279

Dipping, 86Directional

cosine, 260, 457Directions

cosine, 235principal, 595

Dissipation function, 887, 888Drive force

optimal, 74, 75Driveline, 179, 188, 189

clutch, 188di erential, 188drive shafts, 188drive wheels, 188dynamics, 179engine, 188gearbox, 188propeller shaft, 188

Dynamicsdirect, 575

forward, 575indirect, 575inverse, 575Newtonian, 576

Earthe ect of rotation, 574kinetic energy, 607revolution, 607rotation, 607rotation e ect, 291

Eccentric base excitation, 837, 891frequency response, 837, 842mass ratio, 840

Eccentric excitation, 831, 890acceleration, 836eccentric mass, 831eccentricity, 831frequency response, 831mass ratio, 834transmitted force, 837velocity, 836

Eccentricity, 832E ciency, 188

convertor, 188di erential, 193driveline, 189engine, 182mechanical, 190—192overall, 188thermal, 190—192transmission, 188volumetric, 190—192

Eigenvalue, 849Eigenvalue problem, 905

characteristic equation, 905Eigenvector

rst-unit, 906high-unit, 906last-unit, 906normal form, 906normalization, 906

Eigenvector problem, 906Ellipsoid

energy, 588

Index

1049

momentum, 588Energy

conservation , 615, 616Earth kinetic, 607ellipsoid, 588kinetic, 571, 572, 575, 581,

585, 588, 604, 793, 888mechanical, 613, 614potential, 608, 793, 888

Engine, 179Diesel, 180dynamics, 179e ciency, 182front, 189gasoline, 180ideal, 185injection Diesel, 180maximum speed, 198performance, 179rear, 189spark ignition, 180speed, 193torque, 192, 193working range, 200, 211

Envelope, 195Ernesto Cesàro, 436Euler

-Lexell-Rodriguez formula, 262angles, 245—251coordinate frame, 251equation of motion, 580, 584,

586, 589, 591frequencies, 249, 250, 272global rotation matrix, 246inverse matrix, 257local rotation matrix, 246rotation matrix, 245, 246, 257

Euler equationbody frame, 584, 591

Euler, Leonard, 436Eulerian

viewpoint, 287Excitation

base, 808, 819, 1027eccentric, 808, 1027

eccentric base, 808, 1027forced, 808, 809, 1027harmonically, 808, 1027

Flying car, 83Foettinger clutch, 196Foettinger law, 196Force, 568, 573

body, 568centrifugal, 574conservative, 608contact, 568Coriolis, 574, 575e ective, 574external, 568function, 576generalized, 602, 604, 608, 888internal, 568moment of, 568potential, 608resultant, 568rotating, 585time varying, 575total, 568

Force system, 568, 572equivalent, 568, 572

Forced excitation, 809acceleration, 814fequency response, 810transmitted force, 814, 816velocity, 814

FormulaLeibniz, 436relative acceleration, 291Rodriguez, 265

Four wheel steering, 415Four-wheel vehicle, 653

dynamics, 653linearized dynamics, 656

Framecentral, 578principal, 581, 584, 593, 595

Free dynamics, 764Free response, 699, 705, 764Free system, 904

Index

1050

Frequencyangular, 794cyclic, 794damped natural, 852natural , 850nodal, 870ratio, 810response, 808, 810

Frequency ratio, 810Frequency response, 808Fresnel Integrals, 432Freudenstein’s equation, 320, 328Friction

adhesion, 144Burckhardt models, 146cold welding, 144De-Wit models, 146deformation, 144Kiencke and Daviss models,

146Pacejka models, 145wear, 145

Friction ellipse, 168—170Friction mechanisms, 143Friction models, 145, 169Front-engined, 189Front-wheel-drive, 189Front-wheel-steering, 385Fuel

consumption, 183Full car

mode shape, 926natural frequency, 926vibration, 921—923, 926

Functionatan2, 65dissipation, 888Rayleigh, 888signum, 65

G-derivative, 275Gear ratio, 193Gear reduction ratio, 188Gearbox, 192, 193, 198, 200, 201,

203, 205, 207, 211, 212,

215, 216design, 200, 201, 203, 205, 207,

211, 212, 215, 216dynamics, 192geometric, 201, 203, 205, 207,

211, 212progressive, 215, 216stability condition, 198step jump, 201

Gearbox ratio, 188Generalized

coordinate, 602, 604, 605, 609force, 602, 604, 606, 608, 611,

613Global sideslip angle, 646, 650Gough diagram, 154Grasho criterion, 326Grip, 152

Half carantiroll bar, 917, 920mode shape, 919, 920natural frequency, 919, 920vibration, 916—918

Heading angle, 631, 634Helix, 296Hermitian form, 898Homogeneous matrix, 297Hook joint, 369Hydroplaning, 19

dynamic, 19rubber, 20speed, 19, 20viscous, 19

Instant center, 350application, 354coordinate, 357, 358motion, 357, 358number of, 353of acceleration, 361

Inverted slider-crank mechanism,344

acceleration analysis, 349application, 350

Index

1051

coupler point curve, 368input-output, 344possible con gurations, 347velocity analysis, 348

Jackkni ng, 407Jacques Bernoulli, 436Joint, 317

coordinate, 317prismatic, 317revolute, 317universal, 369

Kennedy theorem, 351Kinematics, 233

acceleration, 287Kinetic energy, 571, 572, 588, 604

Earth, 607rigid body, 585rotational body, 581

Kronecker’s delta, 254, 580, 601

Lagrangeequation, 887, 888equation of motion, 601—606,

608mechanics, 608method, 887

Lagrange equationexplicit form, 607

Lagrangean, 608, 609, 887, 888viewpoint, 287

Lane-change maneuver, 768Langensperger, George, 401Lateral acceleration response, 668,

692, 695, 759Lateral velocity response, 669, 680,

692Law

of motion, 571second of motion, 571, 577third of motion, 571

Leibniz formula, 436Leonard Euler, 436Linearized model, 693

oversteer, 696understeer, 696

Link, 317ground, 318

Linkage, 3174-bar, 317coupler link, 318dyad, 328, 335four-bar, 318ground link, 318input angle, 318output link, 318two-link, 328, 335

Location vector, 298, 300, 543Longitudinal force, 139Longitudinal friction, 140Longitudinal slip, 139—141

MacPherson suspension, 506Manganic, 618Manipulator

2R planar, 611one-link, 610

Manjanic, 618Manjaniq, 618Mass center, 569, 572, 577, 578Mass moment

diagonal elements, 598matrix, 591

Matrixangular velocity, 267Euler rotation, 246global rotation, 234local rotation, 240skew symmetric, 256, 261, 267

McPherson suspensionequivalent vibrating model, 939kinematic model, 506

MechanicsNewtonian, 576

Mechanism, 318closed loop, 318instant center, 350inversion, 344inverted slider-crank, 344

Index

1052

open loop, 318parallel, 318pole, 350serial, 318slider-crank, 337steering, 391, 409suspension, 350trapezoidal steering, 391

Mode shape, 904Moment, 568, 573

external, 584resultant, 568, 584total, 568

Moment of inertia, 591about a line, 601about a plane, 601about a point, 601about the origin, 601characteristic equation, 599diagonal elements, 591, 598eigenvalues, 594, 598eigenvectors, 598elements, 591frame-dependent, 592Huygens-Steiner theorem, 594matrix, 591o -diagonal elements, 592parallel-axes theorem, 592—594polar, 591principal, 593, 595, 599principal axes, 581principal invariants, 599product, 592rigid body, 580, 583rotated-axes theorem, 592—594

Moment of momentum, 568, 569Moments of inertia

determination, 862Momentum, 568

angular, 568, 569, 580—584,588

angular , 590ellipsoid, 588linear, 568, 569translational, 569

Natural frequency, 810, 850, 904determination, 862

Neutral distance, 687Neutral steer, 684, 685Neutral steer point, 687Newton

equation in body frame, 578equation of motion, 571, 577,

578, 586, 601equations of motion, 604Lagrange form, 604rotating frame, 574

Onager, 618One-eighth car model, 935, 939

absolute acceleration, 942absolute displacement, 942—

944damping ratio, 936design curve, 971equation of motion, 936excitation frequency, 940frequency response, 942, 945hard suspension, 952, 953model, 803natural frequency, 936optimal characteristics, 955optimal damping, 955optimal design chart, 958optimal design curve, 946, 955,

960optimal sti ness, 955optimal suspension, 953optimization, 946optimization strategy, 946relative displacement, 942—944soft suspensions, 952, 953step input, 968suspension clearance, 952suspension room, 952suspension travel, 952time response, 968, 971trade-o , 960wheel travel , 951, 952working frequency range, 947

Index

1053

Optimizationalternative method, 965cost function, 965design curve, 1002one-eighth car, 935, 946quarter car, 1002RMS, 946, 1002time response, 968, 971transient response, 968, 971trivial, 960vehicle suspension, 954vibration, 865—873wheel travel, 1012

Orthogonality condition, 253Over-damped

vibration, 853, 854Oversteer, 684, 685, 708

Pacejka model, 169Parallelogram suspension, 562Passing maneuver, 768, 771Pendulum

chain, 895double, 893inverted, 806oscillating, 605simple, 289, 605spherical, 609

Physicalquantityvectorial, 569

Pitch moment, 630Planar dynamics, 657, 665

attitude angle, 634body force components, 647characteristic equation, 703coe cient matrix, 697constant lateral force, 688control variables, 660, 664coordinate frame, 629, 630critical speed, 686crouse angle, 634curvature response, 668, 692,

695eigenvalue, 703

force system coe cients, 652,670

free response, 699, 705global sideslip angle, 650heading angle, 634input vector, 660, 664kinematic steering, 652lateral acceleration response,

668, 669, 680, 692, 695linearized model, 693neutral distance, 687neutral steer, 684neutral steer point, 687Newton-Euler, 635Newton-Euler equations, 658oversteer, 684rotation center, 711sideslip coe cient, 648sideslip response, 668, 692stability factor, 684steady state conditions, 695steady-state response, 671, 687,

688steady-state turning, 668step input, 698, 706, 708time response, 696time series, 705transient response, 697understeer, 684vehicle velocity vector, 650wheel number, 632yaw rate response, 668, 692zero steer angle, 699

Plotgear-speed, 205, 207, 212power, 203, 212progressive, 215working range, 203

Pneumatic trail, 150Poinsot’s construction, 588Pole, 305, 350Potential

energy, 572, 608eld, 572force, 608

Index

1054

function, 572kinetic, 609

Powerat wheel, 189constant, 185driveline, 189engine, 189equation, 180friction, 191ideal, 184law, 190maximum, 185peak, 184performance, 179, 180, 182,

184units, 182

Power steering, 413Principal

rotation matrix, 261Principle

conservation of energy, 572superposition, 576

Quadrature, 897, 898asymmetric, 898

Quarter car, 901model, 802natural frequency, 909sprung mass, 909unsprung mass, 909

Quarter car model, 9813-D frequency response, 987body bounce frequency, 995coe cient matrix, 984dimensionless characteristics,

983equations of motion, 982frequency response, 983—985,

993, 995history, 983invariant amplitude, 990invariant frequency, 990, 995main suspension, 981mathematical model, 981

natural frequency, 990, 991,994

nodal amplitude, 992nodal frequency, 991, 992optimal characteristics, 1012optimal design curve, 1002,

1007optimization, 1002optimization strategy, 1003principal natural frequency,

995resonant frequency, 991sprung mass, 981street cars, 985tire damping, 982unsprung mass, 981wheel hop frequency, 995wheel travel, 1012working frequency range, 1004

Rear wheel steering, 396Rear-engined, 189Rear-wheel drive, 189Resonance, 909Resonance zone, 813Ride, 887Ride comfort, 887Rigid body

acceleration, 293angular momentum, 582, 583centroid, 287Euler equation, 584Euler equation of motion, 589kinetic energy, 585moment of inertia, 580, 583moment-free motion, 589motion composition, 266plane motion, 358principal rotation matrix, 598rotational kinetics, 580steady rotation, 586translational, 577velocity, 284, 285

Rim, 1, 3, 21, 22, 24alloy, 24

Index

1055

diameter, 3ange, 22hub, 22hump, 22spider, 22width, 6

Roadbank angle, 66, 68banked, 68clothoid, 432, 433, 449, 453curvature, 433design, 432, 437, 438, 440, 443—

445, 448, 449, 453, 456,458

design chart, 443, 444history, 435inclination angle, 58, 63radius, 433sharpness, 435spatial, 456, 458spiral, 432tangent angle, 433

Road pavement, 134Rodriguez

rotation formula, 262, 263, 265,299, 303

Roll angle, 630, 738Roll angle response, 760Roll axis, 511, 514Roll center, 355, 511, 512Roll dynamics, 737

bicycle model, 748camber trust, 763coe cient matrix, 756control variables, 756, 758curvature response, 759equations of motion, 755, 756force system, 742force system coe cients, 754free dynamics, 764free response, 764hatchback, notchback, station,

775input vector, 758

lateral acceleration response,759

lateral force, 745Newton-Euler equations, 738,

741, 742passing maneuver, 768, 771roll angle response, 760roll damping, 752roll steer, 763roll sti ness, 752roll-steering angle, 745sideslip angle, 745sideslip coe cient, 750slip response, 759steady-state motion, 759steady-state response, 759step input, 766time response, 763tire slip coe cient, 746torque coe cient, 752two-wheel model, 748vehicle slip coe cient, 747wheel force system, 742yaw rate response, 759

Roll height, 514Roll moment, 630Roll sti ness, 517Roll torque, 514Roll-pitch-yaw

global angles, 239, 244global rotation matrix, 239,

244Rolling disc, 892Rolling friction, 128, 130, 131, 135Rolling resistance, 128, 130, 131,

133—136, 138Rotation, 262

about global axis, 233, 238about local axis, 240, 243axis-angle, 260, 262—264direction cosines, 235, 241general matrix, 251global Euler matrix, 257global matrices, 236instantaneous axis, 269

Index

1056

instantaneous center, 287local Euler matrix, 257local matrix, 243local versus global, 258matrix, 238nutation, 245o -center axis, 307order of, 238orthogonality condition, 253pitch, 239pole, 287precession, 245radius of, 386, 388reverse, 262roll, 239roll-pitch-yaw matrix, 244spin, 245successive, 238, 243X-matrix, 234x-matrix, 240Y-matrix, 234y-matrix, 240yaw, 239Z-matrix, 234z-matrix, 240

Rotation matrixelement of, 253

SAE steering de nition, 691Screw, 298, 307

axis, 296central, 297, 298, 300, 302coordinate, 296general, 298left-handed, 297location vector, 297, 298motion, 296parameters, 297, 305pitch, 296principal, 307right-handed, 297rotation, 296special case, 303transformation, 300, 302, 303,

306, 307

translation, 296twist, 296

Second derivative, 282Sideslip angle, 100, 631, 646Sideslip coe cient, 646, 648Sideslip response, 668, 692Sideslip sti ness, 148Slalom, 479Slider-crank mechanism, 337

acceleration analysis, 342, 343coupler point curve, 366input angle, 337input-output, 337limit positions, 343possible con gurations, 340quick return, 344slider position, 337velocity analysis, 340—342

Slip moment, 151Slip ratio, 141Slip response, 759Space

curve, 448Spatial

road, 456, 458Speed equation, 192, 194Speed ratio, 188Speed span, 203Spiral

clothoid, 444Cornu, 436Fresnel, 436transition, 436

Spring, 793linear, 794massive, 800parallel, 796, 797serial, 795sti ness, 794

Stability factor, 684Stall, 57Steady state

center of rotation, 681, 682centripetal acceleration response,

668, 678

Index

1057

curvature response, 668, 672,675

lateral velocity response, 669,670, 680

sideslip response, 668, 676stability factor, 672, 684yaw rate response, 668, 677

Steady state response, 671Steering, 385, 386, 416

4WS factor, 423Ackerman, 458Ackerman condition, 385Ackerman mechanism, 461active steer, 427autodriver, 427bicycle model, 386, 387, 425command, 410comparison, 424counter steer, 420error, 393, 458, 468four wheel, 415—425, 427front wheel, 385independent rear wheel drive,

399inner steer angle, 385, 386,

416inner wheel, 385, 386, 397,

398, 416inner-outer relationship, 386,

391jackkni ng, 407, 469kinematic, 385, 389, 397kinematic condition, 385, 387,

425length, 424locked rear axle, 395, 396maximum radius, 389mechanism, 391, 409—411midline, 403more than two axles, 402, 403multi-link, 462o set, 414optimization, 458, 462, 463,

465, 468

outer steer angle, 385, 386,416

outer wheel, 385, 386, 397,398, 416

passive steer, 427Pitman arm, 409racecars, 400radius of curvature, 423radius of rotation, 390ratio, 410rear wheel, 396reverse e ciency, 413same steer, 420self-steering wheels, 405sign convection, 420, 423sign convention, 416six-wheel vehicle, 403smart steer, 427space requirement, 389, 390,

408speed dependent, 401steer angle, 386steer by wire, 401trapezoidal, 414, 459—461trapezoidal mechanism, 391,

393, 458turning center, 385, 415, 420,

422turning radius, 386—388, 419,

420, 425unequal tracks, 398with trailer, 405, 407, 469—

474, 476—479Steering axis

caster angle, 543caster plane, 544forward location, 544lateral location, 544lean angle, 543lean plane, 544

Steering length, 424Steering mechanisms

drag link, 410, 411lever arm, 410multi-link, 411

Index

1058

optimization, 458, 462, 463,465, 468

parallelogram, 409Pitman arm, 409rack-and-pinion, 410steering wheel, 409tie rod, 410trapezoidal, 459

Steering ratio, 410Step input, 698, 708, 857Step jump, 201Step response, 857

overshoot, 858peak time, 858peak value, 858rise time, 858settling time, 858steady-state, 859

Step steer input, 706, 711Suspension

anti-tramp bar, 497antiroll bar, 508camber, 528camber angle, 521caster, 527caster angle, 543caster plane, 544center, 512Chebyshev linkage, 499De Dion, 504dead axle, 504dependent, 495double A-arm, 506double triangle, 499double wishbone, 506equilibrium position, 519Evance linkage, 499forward location, 544four-bar linkage, 519Hotchkiss, 496independent, 506, 508lateral location, 544lean angle, 543lean plane, 544live axle, 504

location vector, 544McPherson, 506, 939multi-link, 506optimization, 935Panhard arm, 499rest position, 519Robert linkage, 499roll axis, 511roll center, 355, 511, 512S shape problem, 496semi-trailing arm, 508short/long arm, 506solid axle, 495—497, 499, 503,

504spung mass, 496stabilizer, 511steering axis, 543, 544straight line linkages, 499swing arm, 508swing axle, 508toe, 525trailing arm, 508triangulated linkage, 499trust angle, 530twisting problem, 497unsprung mass, 496unsprung mass problem, 503vibration, 935Watt, 499with coil spring, 504

Suspension center, 512Suspension mechanism, 337, 350,

495Chapman, 350double A arm, 337double wishbone, 337dynamic requirement, 532kinematic requirement, 531,

532McPherson, 350

Symbols, xiii

Talbot curve, 436Talbot, Arthur, 436Tangential slip, 141

Index

1059

TheoremChasles, 307, 573Chasles , 296Huygens-Steiner, 594Kennedy, 351, 512parallel-axes, 592, 594Poinsot, 573rotated-axes, 592

Time derivative, 275Time response, 848

free dynamics, 764free response, 764hatchback, notchback, station,

775homogeneous, 849homogeneous solution, 849initial condition, 854, 856initial-value problem, 848non-homogeneous, 849particular solution, 849passing maneuver, 768, 771step input, 766vehicle dynamics, 696, 697,

763Time series, 699, 705Tire, 1, 99

adhesion friction, 143aligning moment, 101, 148, 150—

152, 163American, 7aspect ratio, 3, 6bank moment, 101bead, 11, 13belt, 11bias ply, 3bias-ply, 15blocks, 18bore torque, 101camber angle, 138, 160, 163,

164camber arm, 160camber force, 158, 160camber moment, 160camber sti ness, 159, 165camber torque, 160

camber trail, 160camber trust, 158Canadian, 7carcass, 12circumferential slip, 141cold welding friction, 144combined force, 165combined slip, 168, 169components, 11contact angle, 109coordinate frame, 99, 101, 533cords, 13cornering force, 152cornering sti ness, 148, 152critical speed, 133damping structure, 130de ection, 104deformation friction, 145diameter, 6dissipated power, 135DOT, 2, 7DOT index, 7drag force, 152dynamics, 99E-Mark, 2, 8e ective radius, 107, 109equivalent radius, 110, 141equivalent speed, 140European, 8force system, 100, 165forces model, 169forward force, 100forward velocity, 108friction, 142, 143friction coe cient, 140friction ellipse, 168friction stress, 126function, 17geometric radius, 108, 109grip, 152groove, 12, 18, 19height, 1, 5history, 14hydroplaning, 19hysteresis, 106

Index

1060

in ation, 10in ation pressure, 110, 136,

137inner liner, 11lateral force, 100, 148, 151,

152, 154, 156, 158, 160,161

lateral load, 126lateral ratio, 148lateral sti ness, 149lateral stress, 156, 157light truck, 9load, 109load index, 3, 4load rate, 3loaded height, 108longitudinal force, 100, 139longitudinal friction, 142longitudinal ratio, 148longitudinal slip, 139, 140, 165lugs, 18M&S, 2, 7maximum velocity, 143motorcycles, 135non-radial, 15, 17, 130non-radiale, 164normal force, 100normal load, 123, 125, 126normal stress, 123, 125, 126,

128, 130on a circle, 157overturning moment, 101pitch moment, 101plane, 99plus one, 10pneumatic trail, 150racecar, 133radial, 3, 15, 17, 130radial displacement, 111radiale, 164radius, 6roll moment, 101rolling friction, 128, 130, 131,

135rolling radius, 107, 110

rolling resistance, 128, 130,131, 133—136, 138

rolling resistance torque, 101rubber, 12—15SAE coordinate frame, 102section height, 1section width, 1self aligning moment, 101shallow, 17shear stress, 126side force, 152sideslip, 100sideslip angle, 100, 138, 148,

161, 165sidewall, 1, 10, 12size, 1, 2, 5slick, 133sliding line, 150slip coe cient, 140slip models, 145, 147, 169slip moment, 151slip ratio, 139—143, 145, 147,

165, 169slots, 18spare, 25speed index, 3, 5, 6spring structure, 130sti ness, 103—106, 149strain, 118stress, 118, 123, 125, 126tangential slip, 141tangential stress, 126tilting torque, 101tireprint, 20, 99tireprint angle, 109tireprint model, 164tireprint zone, 110tread, 12, 13, 18, 19, 111, 113tread acceleration, 119tread displacement, 113, 114,

116tread jerk, 120tread travel, 111tread velocity, 113tread wear index, 9

Index

1061

tube-type, 17tubeless, 17type index, 2UTQG index, 9vertical force, 100voids, 18wear, 21wear friction, 145weight, 6wheel load, 100width, 1, 2, 6yaw moment, 101

Tireprint, 20, 21, 100, 123, 125,164

angle, 109force, 517position, 547

Toe, 525Toe-in, 525Toe-out, 525Torque, 568

at wheel, 190, 193equation, 180maximum, 185peak, 184performance, 180, 182, 193

Track, 386Traction

force, 192Traction equation, 192, 194Trailer, 60, 65Transformation

general, 251tire to vehicle frame, 540tire to wheel frame, 535, 536tire to wheel-body frame, 537wheel to tire frame, 533, 536wheel to wheel-body frame,

539wheel-body to vehicle frame,

542Transformation matrix

elements, 254Transient response

free dynamics, 764

free response, 764hatchback, notchback, station,

775passing maneuver, 768, 771step input, 766vehicle dynamics, 697, 763

Transmission ratio, 188, 189, 193Transmission ratios, 198Trapezoidal steering, 391, 393Tread, 18, 19

grooves, 18lugs, 18slots, 18voids, 18

Trebuchet, 616Trigonometric equation, 64Trochoid, 539Trust angle, 530Turning center, 415, 420, 422Two-wheel vehicle, 647, 652, 657,

665, 668, 693, 755body force components, 647camber trust, 763characteristic equation, 703coe cient matrix, 697, 756constant lateral force, 688control variables, 660, 664, 756,

758coordinate frame, 629, 630critical speed, 686curvature response, 668, 692,

695, 759eigenvalue, 703equations of motion, 755, 756force system coe cients, 652,

670, 754free dynamics, 764free response, 699, 705, 764global sideslip angle, 650hatchback, notchback, station,

775input vector, 660, 664, 758kinematic steering, 652lateral acceleration response,

668, 669, 680, 692, 695,

Index

1062

759linearized model, 693neutral distance, 687neutral steer, 684neutral steer point, 687Newton-Euler equations, 658oversteer, 684passing maneuver, 768, 771roll angle response, 760roll damping, 752roll steer, 763roll sti ness, 752rotation center, 711sideslip coe cient, 648, 750sideslip response, 668, 692slip response, 759stability factor, 684steady state conditions, 695steady-state motion, 759steady-state response, 671, 687,

688, 759step input, 698, 706, 708, 766time response, 696, 763time series, 705torque coe cient, 752transient response, 697understeer, 684vehicle velocity vector, 650yaw rate response, 668, 692,


Under-dampedvibration, 853, 854

Understeer, 684, 685, 706Unit system, xiiUniversal joint, 369, 371—373, 375—

377double, 375history, 377speed ratio, 373, 375

vd2f-119, 118Vecface, 570Vecfree, 570

Veclane, 570Vecline, 570Vecpoface, 570Vecpoint, 570Vecpolane, 570Vecpoline, 570Vecporee, 570Vector

axis, 569bounded, 570characteristics, 569de nition, 569direction, 569, 570end point, 569free, 570length, 569line, 570line of action, 569, 570plane, 570point, 570point-free, 570point-line, 570point-plane, 570requirements, 569sliding, 570start point, 569surface, 570types, 569vecface, 570vecfree, 570vecline, 570vecpoface, 570vecpoint, 570vecpolane, 570vecpoline, 570vecporee, 570

Vehicle, 26accelerating, 50, 52, 53, 55,

57, 58braking, 49classi cations, 26curb weight, 29FHWA classi cations, 26gross weight, 31ISO classi cations, 26

Index

1063

longitudinal dynamics, 39, 40,43—45, 47—50, 52, 53, 55,57, 58, 65, 66, 68, 70, 74—76, 79, 81, 83, 84, 86, 88,93

mass center, 75mass center position, 40, 41,

43, 44, 93maximum acceleration, 53, 57,

58more than two axles, 76, 79on a banked road, 66, 68on a crest, 81, 83, 84on a dip, 86, 88on a level pavement, 39on an inclined pavement, 45,

49optimal brake force, 70, 74,

75optimal drive force, 70, 75passenger car classi cations,

29, 31size classi cations, 29stall, 57weight classi cations, 29wheel loads, 40wheel locking, 76with a trailer, 60, 65

Vehicle dynamics180 deg quick turn, 665, 666aligning moment, 630attitude angle, 631, 634bank moment, 630bicycle model, 647, 649, 657,

665, 668, 693, 748body force components, 647body force system, 642camber trust, 763characteristic equation, 703coe cient matrix, 697, 756coe cients matrix, 660, 664constant lateral force, 688control variables, 660, 664, 756,

758critical speed, 686

crouse angle, 631, 634curvature response, 668, 692,

695, 759direct, 698eigenvalue, 703equations of motion, 649, 755,

756force system, 630, 742force system coe cients, 651,

652, 670, 754forward, 698forward force, 630four-wheel-steering, 661free dynamics, 764free response, 699, 705, 764front-wheel-steering, 694general motion, 742hatchback, notchback, station,

775heading angle, 631, 634indirect, 698input vector, 660, 664, 758inputs vector, 664inverse, 698Lagrange method, 637lateral acceleration response,

668, 669, 680, 692, 695,759

lateral force, 630, 646, 651,655, 745

lateral moment, 630linearized model, 693, 695longitudinal force, 630neutral, 684, 685neutral distance, 687neutral steer, 684neutral steer point, 687Newton-Euler, 635Newton-Euler equations, 658,

738normal force, 630oversteer, 684, 685overturning moment, 630passing maneuver, 768, 771path of motion, 639

Index

1064

pitch angle, 630, 738pitch moment, 630pitch rate, 630, 738planar, 629principal method, 639rear-wheel-steering, 665rigid vehicle, 629, 737roll angle, 630, 738roll angle response, 760roll damping, 752roll dynamics, 737, 738, 742roll moment, 630roll rate, 630, 738roll rigid vehicle, 742roll steer, 763roll sti ness, 752roll-steering angle, 745rotation center, 711SAE steering de nition, 691second-order equations, 722sideslip angle, 631, 745sideslip coe cient, 648, 750sideslip coe cients , 646sideslip response, 668, 692six DOF, 741slip response, 759stability factor, 684steady state conditions, 695steady-state motion, 759steady-state response, 671, 687,

688, 759steady-state turning, 668steer angle, 649step input, 698, 706, 708, 766step steer input, 711tilting torque, 630time response, 696, 706, 708,

763time series, 699, 705tire force system, 642tire lateral force, 646tire slip coe cient, 746torque coe cient, 752traction force, 630transient response, 697, 763

two-wheel model, 647, 649, 657,665, 668, 693, 748

understeer, 684, 685vehicle load, 630vehicle slip coe cient, 747vehicle velocity vector, 650vertical force, 630wheel force system, 742wheel frame, 643wheel number, 632yaw angle, 630, 738yaw moment, 630yaw rate, 630, 738yaw rate response, 668, 692,


Vehicle vibration, 887alternative optimization, 965antiroll bar, 917, 920base excited model, 935bicycle car, 911, 914, 915body pitch, 911body roll, 916—918bounce, roll, and pitch, 921dissipation function, 888driver, 901excitation frequency, 940frequency response, 942full car, 921—923half car, 916—918Lagrange equation, 888Lagrange method, 888McPherson suspension, 939mode shape, 904, 919, 920,

926natural frequenc, 926natural frequency, 904, 919,

920one-eighth model, 935optimal design curve, 946optimization, 935optimization strategy, 946quadrature, 897quarter car, 901, 981sprung mass, 935

Index

1065

time response, 968, 971wheel travel , 951, 952working frequency range, 947

Velocitybody point, 573

Vibration1/8 car model, 803absorber, 865amplitude, 810angular frequency, 794angular lag, 810application, 860base excitation, 808, 819, 1027beating, 817characteristic equation, 905cyclic frequency, 794damping ratio, 810discrete model, 801displacedspring, 939dynamic amplitude, 813eccentric base excitation, 808,

1027eccentric excitation, 808, 1027eigenvalue problem, 905eigenvector problem, 906equilibrium position, 801Equivalent system, 803excitation, 795forced, 795, 813forced excitation, 808, 1027Frahm absorber, 866—873Frahm damper, 866—873free, 854, 856free system, 904frequency ratio, 810frequency response, 808, 810,

814harmonic, 795initial condition, 854, 856isolator, 865lumped model, 801measurement, 860mechanical, 793natural frequency, 810Newton’s method, 801

nontrivial solution, 905optimization theory, 865—873orthogonality functions, 817periodic, 795phase, 810quarter car model, 802random, 795resonance zone, 813rest position, 905ride comfort, 887stable, 802static amplitude, 813steady-state solution, 808step input, 857tilted spring, 937—939transient, 795transmitted force, 816, 829trivial solution, 905two-DOF base excited, 805unstable, 802vehicle, 887work of a harmonic force, 856

Virationcharacteristic equation, 849characteristic parameters, 849critically-damped, 853damped natural frequency, 852eigenvalues, 849forced, 849forced classi cation, 843free, 849initial-value problem, 848natural frequency, 850, 851over-damped, 853time response, 848, 850transient response, 850under-damped, 853

Virtualdisplacement, 604work, 604

Wheel, 21, 22angular velocity, 108camber angle, 531coordinate frame, 531, 533

Index

1066

degrees-of-freedom, 531ange, 21forward velocity, 108history, 25non-steerable, 531spider, 21spin, 531steer angle, 531steerable, 531wire spoke, 24

Wheel number, 632Wheel travel, 951

lower, 952upper, 952

Wheel-bodycoordinate frame, 533

Wheelbase, 386Windshield wiper, 328

double-arm opposing, 328double-arm parallel , 328sweep angles, 331

Work, 571, 572, 575virtual, 604

Work-energy principle, 572Wrench, 572

Yaw moment, 630Yaw rate response, 668, 692, 759Yaw velocity, 395Yoke joint, 369

Zero steer input, 699Zero velocity point, 286

Index

Documents

References - link.springer.com3A978-1... · References Abe,M.,2009, VehicleHandlingDynamics:TheoryandApplication ,Butterworth-Heinemann, Oxford, UK. Alkhatib, R., Jazar, R. N., and