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## Homework Statement

A particle of mass m is on top of a frictionless hemisphere centered at the origin with radius a"

Set up the lagrange equatinos determine the constraint force and the point at which the particle detaches from the hemisphere

## Homework Equations

L=T-U

## The Attempt at a Solution

this is NOT HW

solution is there in full (example from book) I am just trying to understand

why is φ not one of the proper generalized coordinates? can't the particle move sideways as well when released? shouldn't the GC be (r,θ,φ) ie all spherical and the constraint equation r-a=0.

THanks