Hamel's Formalism And Variational Integrators On A Double Spherical Pendulum

Hamel's formalism is a general representation of Lagrange mechanics by using a pair of independent non-canonical variables in the velocity phase space.Hamel variational integrators,derived from the discrete Hamilton's principle in Hamel's formalism,have excellent performance for mechanics systems in exponentially long time in preserving(nonholonomic)constraints,energy,momentum etc.First,in this thesis,it is introduced that the general frame of Hamel variational integrators.Next,the Hamel equations and the Hamel variational integrators are obtained for a simple interconnected system,the double spherical pendulum.In contrast to the simulations of the Hamel equations by using the Runge-Kutta method,it is verified that Hamel variational integrators have desired performances of energy preserving and length constraint preserving in exponentially long time with high precision by numerical simulations of the Hamel variational integrators.Finally,another discrete equations of the double spherical pendulum are derived by the Legendre transformation.