MthtttttbyceThe Frenet frame Boat,

hit it falls got for canes tht saethshe zero auntie, e.g. ,

#so it's ftn safe to he otr fans : orthglwmrswldet = 't

Df : A family f Ns) is a mp F : I →5013¥ st .

the first column of Hs) is a' b)

.

<Fi

9

Fz

EnteEs

' F,

Br the Fretter,

F .

- ( Iniis, } & F

'= F [ Kong :D

← to BkDtgspgffhefedmtm

the

Pq : If F is a fine,

F'

= FS fr se Shu . syndic S.

Now,

lets syF Bse

smooth fmyf an odyk Paaetroed one &,

& define the veetrfdd

Vb) = cos as ) Fds) + sin Ots) Els )

¥i**VIS)

Nn,

it wald be good to find the mini mtf - twisty sh vf.

Sine V is a mituf.

,it dnbte aptyhomh it ,

twisty

Road tht FYSK Fly Sls )

aatH H # ii. '⇒ Easy:⇒

• V '

b) = - an Ots) 0' b) Eds) + cosots) Fils) + usotslo ' # Fds) + snots) Fils )

= -SMOHOYSI EG) t cosots) 4,261Fils) - d ↳ b) FDA +650406 ) Fsb) TSMOH(a , ,Fils) tazds) Fzls) )

=/ a ,ds) costs) +2,36 ) sm Ots)) Fils) + (2236km Hsl - Shah 0 ' Isl) Els) + loosest Ok) - ads ) costs)) Fsls)

So the off . f Fz is SMHS ) ( Lists - 0 ' b)) & off . f Fs B asotsll OH - Lids ))

so if we ht 0 's ) .

- ads ) & mtgte to at as ),

need p w/ a frae F st. F. ↳KHS) & FIGFV '

G) = Xs) FT b)

= Xls) Tls)

from flim X.

Now,

# dyads athe mitlafe 00=0+0)

,

htoth.se Bopletf defined : f Zshfms he inittgledifhie boo,

the the gle dike is He sat alls

.

we all the fne Ftc Bishop the wte relatively pnlldadaptdfme (RPAFS.

F ¥€structure guts : Iffirm . C t

,H

HEtookit}k

z

i. e.,

T 's k,

F,

t k, Fz

' II. ifThe fdisk ,

& ku one the awake & tersin : Ns ) = It' G) I = itkks )2 - K is the radius in the k.kz - plan

.

Nb) = TH¥,,

= # ) E t HE) Fs = cos 0 Et

SnoFs

I 959mg Sun to I

yk B =T×N = T×lasO Fztsn 0 B) THE - Sm O Fz

/so TGKN 's) . Bls) :( 0

'b) tsmo E host FD + smethymtdicdm) . B± O

'b),

or 061=5 Hslds.

Since cos a .

- ha ,& Sm O = far ,

he see tht STGIB is the polar ape in the k.kz . plane