32 citations · 72 across the 7 of their papers we have counts for
7 papers
Homogeneity and projective equivalence of differential equation fields
M. Crampin, D. J. Saunders
We propose definitions of homogeneity and projective equivalence for systems of ordinary differential equations of order greater than two, which allow us to generalize the concept…
Reduction of invariant constrained systems using anholonomic frames
M. Crampin, T. Mestdag
We analyze two reduction methods for nonholonomic systems that are invariant under the action of a Lie group on the configuration space. Our approach for obtaining the reduced equa…
The inverse problem for Lagrangian systems with certain non-conservative forces
T. Mestdag, W. Sarlet, M. Crampin
We discuss two generalizations of the inverse problem of the calculus of variations, one in which a given mechanical system can be brought into the form of Lagrangian equations wit…
On the generalized Helmholtz conditions for Lagrangian systems with dissipative forces
M. Crampin, T. Mestdag, W. Sarlet
In two recent papers necessary and sufficient conditions for a given system of second-order ordinary differential equations to be of Lagrangian form with additional dissipative for…
Routh's procedure for non-Abelian symmetry groups
M. Crampin, T. Mestdag
We extend Routh's reduction procedure to an arbitrary Lagrangian system (that is, one whose Lagrangian is not necessarily the difference of kinetic and potential energies) with a s…
The inverse problem for invariant Lagrangians on a Lie group
M. Crampin, T. Mestdag
We discuss the problem of the existence of a regular invariant Lagrangian for a given system of invariant second-order differential equations on a Lie group , using approaches b…