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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 $r\leq a$ (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?

Qmechanic
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Mr.Gandalf Sauron
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1 Answers1

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  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.
Qmechanic
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