A Student's Guide to Lagrangians and Hamiltonians by Hamill Patrick

Author:Hamill, Patrick [Hamill, Patrick]
Language: eng
Format: epub
Publisher: Cambridge University Press
Published: 2013-11-30T00:00:00+00:00

where the As are known functions of the qs. If this relation holds for the dqs, it will also hold for the δqs, so we can write

(3.18)

But this last expression has the same form as the expression for δf for a holonomic constraint, which we wrote as

Therefore, we can use exactly the same reasoning as before, simply replacing the with As. (Note, however, that although the As are known quantities, they are not partial derivatives of some known function.) Consequently, if our single non-holonomic constraint can be expressed as in Equation (3.18), the Lagrange equations are

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