Optimal control problems for underactuated mechanical systems can be seen as a higher-order variational problem subject to higher-order constraints (that is, when the Lagrangian function and the constraints depend on higher-order derivatives such as the acceleration, jerk or jounces). In this paper we discuss the variational formalism for the class of underactuated mechanical control systems wh...

We consider structure preserving numerical schemes for the Ostrovsky equation, which describes gravity waves under the influence of Coriolis force. This equation has two associated invariants: an energy function and the L norm. It is widely accepted that structure preserving methods such as invariants-preserving and multi-symplectic integrators generally yield qualitatively better numerical res...

The importance of nonlinear beam dynamics effects in synchrotron light sources is caused by strong demands on beam quality to obtain long lifetime, small emittance and stability. In this paper, the non-linear particle trajectory equation modifications are given, which simplify the single particle tracking simulation in storage ring using the Matlab environment [1]. The radiation damping times i...

We consider two related problems arising from a question of R. Graham on quasirandom phenomena in permutation patterns. A “pattern” in a permutation σ is the order type of the restriction of σ : [n] → [n] to a subset S ⊂ [n]. First, is it possible for the pattern counts in a permutation to be exactly equal to their expected values under a uniform distribution? Attempts to address this question ...