- #1
jamie.j1989
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Homework Statement
I've thought of a problem to help me with Lagrange multipliers but have got stuck.
Consider a particle of mass m moving on a surface described by the curve y = x2, the particle is released from rest at t = 0 and a position x = l. I'm trying to work out the EOM's but have got stuck.
Homework Equations
[itex]\grave{L}[/itex] = T - V - λ(y - x2)
T = [itex]\frac{1}{2}[/itex]m([itex]\dot{x}[/itex]2+[itex]\dot{y}[/itex]2)
V = -mgy
The Attempt at a Solution
The Euler Lagrange equations give,
m[itex]\ddot{x}[/itex] = 2λx (1)
m[itex]\ddot{y}[/itex] = mg - λ (2)
attempt at solving for (1)
x = Asinh(kt) + Bcosh(kt)
which gives
k = [itex]\sqrt{\frac{2λ}{m}}[/itex]
initial conditions give A = 0, B = l
This is where I get confused, I don't understand how the solution is cosh, surely it would be sinusoidal? And I'm unsure how to solve for λ? Thanks.