a) Define a holonomic constraint and explain the impact of such constraints on the number of degrees of freedom of a system. Give an example of a non-holonomic constraint.
a) Define a holonomic constraint and explain the impact of such constraints on the number of degrees of freedom of a system. Give an example of a non-holonomic constraint.
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a) Define a holonomic constraint and explain the impact of such constraints on the
number of degrees of freedom of a system.
Give an example of a non-holonomic constraint.
b) Five identical flat circular plates are served on a circular conveyor belt. The plates
have mass m, radius 5 cm and moment of inertia Ip about their axis of symmetry.
They are free to move under gravity on top of a conveyor belt which has inner radius
a, outer radius b and moment of inertia Ic about a vertical axis through its centre.
From above, it looks like the diagram below.
a
The belt is banked at a fixed angle a such that the inner edge is lower than the
outer edge. Assuming the conveyor belt rotates freely, how many degrees of freedom
does this system have?
Find the Lagrangian for the system. Hence find and identify any conserved quanti-
ties of the system.
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