Invariant tori and Lagrange stability of pendulum-type equations

Invariant Euler-Lagrange Equations and the Invariant Variational Bicomplex

In this paper, we derive an explicit group-invariant formula for the EulerLagrange equations associated with an invariant variational problem. The method relies on a group-invariant version of the variational bicomplex induced by a general equivariant moving frame construction, and is of independent interest. Mathematics Subject Classification (2000): Primary: 53A55, 58J70, 58E40 Secondary: 35A...

Degenerate Equations of Pendulum-type

Orthogonal stability of mixed type additive and cubic functional equations

In this paper, we consider orthogonal stability of mixed type additive and cubic functional equation of the form $$f(2x+y)+f(2x-y)-f(4x)=2f (x+y)+2f(x-y)-8f(2x) +10f(x)-2f(-x),$$ with $xbot y$, where $bot$  is orthogonality in the sense of Ratz.

Invariant Lagrangians , mechanical connections and the Lagrange - Poincaré equations

We deal with Lagrangian systems that are invariant under the action of a symmetry group. The mechanical connection is a principal connection that is associated to Lagrangians which have a kinetic energy function that is defined by a Riemannian metric. In this paper we extend this notion to arbitrary Lagrangians. We then derive the reduced Lagrange-Poincaré equations in a new fashion and we show...

Subharmonic Oscillations of Forced Pendulum-Type Equations

where f is periodic with minimal period T and mean value zero. We have in mind as a particular case the pendulum equation, where g(x) = A sin x. First results on the existence of subharmonic orbits in a neighborhood of a given periodic motion were obtained by Birkhoff and Lewis (cf. [3] and [ 143) by perturbation-type techniques. Rabinowitz [ 151 was able to prove the existence of subharmonic s...