Lagrange equations of the first kind

[saRisky]

Homework Statement

A material point of mass m is moving in a constant gravitational field along the intersection of a sphere and a moving plane (z=Rsin(omega*t)). Find Lagrange's equations (first kind), the point's movement, and the constraint forces. Ignore friction and assume that the gravitational field is parallel to the "z" axis.

Relevant Equations

Lagrange equations of first kind

We cannot make it anyhow

 

[anuttarasammyak]

If I take the setting correctly, gravity force (z direction ) is always perpendicular to free degree motion of the body ( on xy plane ) so it makes no effect to the motion. Only the inflating-shrinking circle boundary of the intersection would matter.