Math help needed!

[phatcat600 10+ year member]

We are dealing with arc length and normal and binormal vectors.

45) Show that the curvature k is related to the tangent and normal vectors by the equation dT/ds=kN.

47) a) show that dB/ds is perpendicular to B.

b) show that dB/ds is perpendicular to T.

c) Deduce from parts (a) and (b) that dB/ds=-t(s)N for some number t(s) called the torsion of the curve. (the torsion measures the degree of twisting of a curve.)

d)Show that for a plane curve the torsion is

t(s)=0

48) The following formulas, called the Frenet-Serret formulas are of fundamental importance in differential geometry.

1) dT/ds=kN

2) dN/ds=-kT+tB

3) dB/ds=-N

(Formula 1 comes from excercise 45 and formula 3 comes from excercise 47.) Use the fact that N=BxT to deduce formula 2 from formulas 1 and 3.

Im not looking for exact answers but any help would be appreciated. I dont even know where to start these. Thanks a lot. I didnt get any useful responses on yahoo answers //content.invisioncic.com/y282845/emoticons/frown.gif.a3531fa0534503350665a1e957861287.gif

Click to read more...

 

[brtnboarder3241 5,000+ posts]

shit i think i kno the answer.. its hard as **** though.

 

[phatcat600 10+ year member]

Seriously? If you can help at all it would be great, even little tips because I am completely stumped. I dont even know where to start.

 

[brtnboarder3241 5,000+ posts]

i forgot.

 

[phatcat600 10+ year member]

Not funny man I thought I had a chance for a second. Anybody know any good forums to look for this stuff?

 

[brtnboarder3241 5,000+ posts]

hotmath.com ?

 

[dB-SPL 10+ year member]

Would you possibly have any numbers to substitute the equation?

-Bill-

 

[phatcat600 10+ year member]

Nope, thanks for the reply. That is it. I will list some of the equations I know that are supposed to help

ds/dt=|r'(t)| N=T'(t)/|T'(t)| k=|T'(t)|/|r'(t)|

T is the unit tangent vector

N is the unit normal vector and

B is the binormal vector

 

[phatcat600 10+ year member]

What happened guys? Why no more responses?

 

[dB-SPL 10+ year member]

I'm not going to try to explain such a complex formula as I would rather not be the cause of failure if I am wrong. But this may help you understand. Hope that helps. //content.invisioncic.com/y282845/emoticons/frown.gif.a3531fa0534503350665a1e957861287.gif

http://en.wikipedia.org/wiki/Frenet-Serret_formulas

-Bill-

 

[phatcat600 10+ year member]

No I looked at that already. Can you give any guidance? Even if you are totally wrong it will still give me ideas or a new way to look at it. Anything at all helps, I mean it. I dont know where to go from here.

 

[phatcat600 10+ year member]

anybody? my teacher gave me the hint to look at the chain rule to figure out what is going on

 

[terra 5,000+ posts]

this is one hard *** mofo of a problem. im in honors physics too...