A sphere of radius p is constrained to roll without slipping on the lower half of the inner surface of a hollow cylinder of inside radius R. Determine the Lagrangian function, the equation of constraint, and Lagrange's equations of motion. Find the frequency of small oscillations.
A sphere of radius p is constrained to roll without slipping on the lower half of the inner surface of a hollow cylinder of inside radius R. Determine the Lagrangian function, the equation of constraint, and Lagrange's equations of motion. Find the frequency of small oscillations.
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Theoretical Mechanics
Topic: Lagrangian and Hamiltonian Dynamics
>Generate the necessary equations to this system.
> Use the equations of motion
>Generate equations for (x,y), (Vx,Vy), V², T
> L = T-U
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For study purposes. Thank you!
Transcribed Image Text:7-3.
A sphere of radius p is constrained to roll without slipping on the lower half of the
inner surface of a hollow cylinder of inside radius R. Determine the Lagrangian
function, the equation of constraint, and Lagrange's equations of motion. Find the
frequency of small oscillations.
.
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