(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The skier is skiing without friction down the mountain, being all the time in a specified plane. The skier's altitude y(x) is described as a certain defined function of parameter x, which stands for the horizontal distance of the skier from the initial position. The skier is subjected to gravity g = -g e_{y}.

a) Calculate forces of constraint in relation to x.

b) Prove that if the skier can detach from the mountain at a point with horizontal value x_{od}, then y''(x_{od}) < 0, i.e. function y(x) is concave in this point.

Use first kind Lagrange equations (Lagrange multipliers).

2. Relevant equations

3. The attempt at a solution

To be honest I am completely lost. This is so abstract with not even a function given that I don't know how to specify the initial constraint equation. Normally there would be y and x in it, so I wrote f(x,y) = y - y(x) = 0, which feels weird ...

I wrote the Lagrange equations based on that weird constraint, but even if that would be good I have no idea how to get Lambda from that :(

I started doing masters in physics after finishing bachelor in mechatronics, and compared to physics students I have huge gaps in knowledge (even though classical mechanics is a 2nd year subject here).

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# Homework Help: Lagrange Multipliers in Classical Mechanics - exercise 1

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