-
7/24/2019 EGCE 302-(4) Chapter 11 Alternate Coordinate
Systems-C-2
1/20
1
DynamicsEGCE 302
Spring 2016
California State University, Fullerton
Department of Civil and Environmental Engineering
Nagi Abo-Shadi, PhD, PE, SE, PEng
Chapter
Alternate Coordinate Systems
-
7/24/2019 EGCE 302-(4) Chapter 11 Alternate Coordinate
Systems-C-2
2/20
2
Tangential and Normal Coordinates
Still working with curvilinear motion
- In the previous lecture we used (i, j, k) as unit vectors
- Now, we will use unit vectors along the curved path suchas
(etand en)
- n stands for Normal
- t stands for Tangential
-
7/24/2019 EGCE 302-(4) Chapter 11 Alternate Coordinate
Systems-C-2
3/20
3
Velocity
The velocity is in the tangential direction only.
Therefore:
Acceleration
The acceleration is determined by differentiating the
velocity
with respect to the time (t)
Therefore:
-
7/24/2019 EGCE 302-(4) Chapter 11 Alternate Coordinate
Systems-C-2
4/20
4
Therefore:
-
7/24/2019 EGCE 302-(4) Chapter 11 Alternate Coordinate
Systems-C-2
5/20
5
Finally:
The acceleration will have two (2) components in both
thetangential and normal directions to the curve path, as
follows:
-
7/24/2019 EGCE 302-(4) Chapter 11 Alternate Coordinate
Systems-C-2
6/20
6
Required:
3
Example
-
7/24/2019 EGCE 302-(4) Chapter 11 Alternate Coordinate
Systems-C-2
7/20
7
3
As previously determined,
3
3 3 3 32.2/ 80
87.9 /
-
7/24/2019 EGCE 302-(4) Chapter 11 Alternate Coordinate
Systems-C-2
8/20
8
Example
!
-
7/24/2019 EGCE 302-(4) Chapter 11 Alternate Coordinate
Systems-C-2
9/20
9
(speed
is
increasing)
(speed
is
decreasing)
(a)Sincevelocitiesareknown
/
Use
component
(nongeometric)
option
-
7/24/2019 EGCE 302-(4) Chapter 11 Alternate Coordinate
Systems-C-2
10/20
10
i + 0j
)Cos i +( 540)Sin
i 468
j
-
7/24/2019 EGCE 302-(4) Chapter 11 Alternate Coordinate
Systems-C-2
11/20
11
(b)Accelerationspartiallyknown
(straightlineat
i
+
+
+
112.5
m/
( 3Cos i +3Sin )+
( 112.5
Cos
i 112.5
Sin j)
99
i 53.7
j
-
7/24/2019 EGCE 302-(4) Chapter 11 Alternate Coordinate
Systems-C-2
12/20
12
Therefore:
/
/
i 54m/ j
-
7/24/2019 EGCE 302-(4) Chapter 11 Alternate Coordinate
Systems-C-2
13/20
13
Radial and Transverse Coordinates
Still working with curvilinear motion
- In the previous lecture we used (i, j, k) as unit vectors
- Now, we will use unit vectors along the curved path suchas
(erand e)
- r stands for Radial
- t stands for Transverse
-
7/24/2019 EGCE 302-(4) Chapter 11 Alternate Coordinate
Systems-C-2
14/20
14
Velocity
-
7/24/2019 EGCE 302-(4) Chapter 11 Alternate Coordinate
Systems-C-2
15/20
15
Acceleration
-
7/24/2019 EGCE 302-(4) Chapter 11 Alternate Coordinate
Systems-C-2
16/20
16
Conclusion
-
7/24/2019 EGCE 302-(4) Chapter 11 Alternate Coordinate
Systems-C-2
17/20
17
Example
-
7/24/2019 EGCE 302-(4) Chapter 11 Alternate Coordinate
Systems-C-2
18/20
18
Determine
velocity
and
acceleration
at
(a)t=0sec and (b)t=5sec
-
7/24/2019 EGCE 302-(4) Chapter 11 Alternate Coordinate
Systems-C-2
19/20
19
=2(2Cos
. Sin t
=
4
(2
Cos
2
t
2(2Cos
0
-
7/24/2019 EGCE 302-(4) Chapter 11 Alternate Coordinate
Systems-C-2
20/20
20
+r
+
) +(r +2 )
+
(0
+
0)
When t=5sec,trythisathome
