Homework Help: Motion of a particle on a saddle surface under gravity

1. Feb 24, 2010

yanyan_leung

I have encountered a problem which needed to solve the below differential equation. The question is to solve the motion of a point mass on the xy=z surface using the Lagrangian. The exact question is as follow: A partical of mass m is constrainted to move under gravity with no friction on the surface xy=z. What is the trajectory of the particle if it starts from rest at (x,y,z) = (1, -1, -1) with the z-axis vertical.

And I have solved the following equation of motions:
$$z\ddot{z}=mg+m\lambda$$
$$x\ddot{x}=y\ddot{y}=C$$, where c is a constant

Thanks!!