# Lagrange dynamics of a rolling ball inside a hollow cylinder

A sphere of radius r is constrained to roll without slipping on the inner surface of the lower half of a hollow cylinder of inside radius R.

Determine the following:

a) the Lagrangian function.

b) The equation of constraint

c) Lagrange's equation of motion

d) Frequency of SMALL oscillations

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A sphere of radius r is constrained to roll without slipping on the inner surface of the lower half of a hollow cylinder of inside radius R.

Determine the following:

a) the Lagrangian function.

b) The equation of constraint ...

#### Solution Summary

Great example of using Lagrange dynamics. I have provide detailed step in solving this problem in a 3-page word document.