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 ey.
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 xod, then y''(xod) < 0, i.e. function y(x) is concave in this point.
Use first kind Lagrange equations (Lagrange multipliers).
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).