springo
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Hey guys so I had trouble with this problem, I hope it's not too long and you can help me out.
A point moves following (starting at λ = 0 and increasing):
x = 4·cn(λ)
y = 3·sn(λ)
z= am(λ)
Find the distance the point has traveled when the speed vector is parallel to (-4, 3, √2).
The elliptic functions are of the first kind with k2 = 1/2.
I thought of the following:
v = dp/dt = (-4·sn(λ)·dn(λ), 3·cn(λ)·dn(λ), dn(λ))·(dλ/dt) = c·(-4, 3, √2) (with c a constant real number)
But then I don't know what to do next...
Thank you so much for your help!
Homework Statement
A point moves following (starting at λ = 0 and increasing):
x = 4·cn(λ)
y = 3·sn(λ)
z= am(λ)
Find the distance the point has traveled when the speed vector is parallel to (-4, 3, √2).
Homework Equations
The elliptic functions are of the first kind with k2 = 1/2.
The Attempt at a Solution
I thought of the following:
v = dp/dt = (-4·sn(λ)·dn(λ), 3·cn(λ)·dn(λ), dn(λ))·(dλ/dt) = c·(-4, 3, √2) (with c a constant real number)
But then I don't know what to do next...
Thank you so much for your help!