2010•arXiv (Cornell University)Open access
On the compatibility of non-holonomic systems and certain related\n variational systems
C. Cronström
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Abstract
I consider the equations of motion which follow from d'Alembert's principle\nfor a general mechanical system in a space of N dimensions, constrained by a\nnon-holonomic constraint which is linear and homogeneous in the generalised\nvelocities. The variational equations of motion which follow for the same\nsystem by assuming the validity of a specific variational action principle, in\nwhich the non-holonomic constraint is implemented by means of the\nmultiplication rule in the calculus of variations are also considered. It is\nshown that these two types of equations of motion are not compatible in a space\nof dimension N greater than or equal to 3, if the constraint is genuinely\nnon-holonomic. This means that these two types of equations of motion do not\nhave coinciding general solutions.\n
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