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Definition/classification of holonomic and non-holonomic constraints

Physics Asked by Arghyadeep Chatterjee on August 1, 2021

I am a mathematics student. I have Lagrangian and Hamiltonian mechanics as an elective I have taken in this sem. Today I had a test in which I was asked a question:

  1. A ball is constrained to move inside a spherical cage. The constraint imposed by the cage is (a) Non-holonomic (b) Holonomic (c) Rheonomic (d) None of these.

I gave the answer as none of these as I thought that constraints imposed by an inequality $rleq a$ (where $r$ denotes distance from origin and a denotes radius of sphere) is unilateral in nature.
But I am told that the answer would be non-holonomic.
Now I was a bit confused as nothing was mentioned about the velocity or time or anything on which the motion would depend inside the sphere. What should be the answer? Is non-holonomic correct?

One Answer

  1. Ref. 1 defines a non-holonomic constraint as the opposite of a holonomic constraint.

  2. Ref. 1 mentions that inequalities (aka. one-sided constraints) are examples of non-holonomic constraints.

  3. For completeness, let us also mention semi-holonomic constraints.

References:

  1. H. Goldstein, Classical Mechanics; Section 1.3.

Correct answer by Qmechanic on August 1, 2021

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