A new approach to the solution of optimal control problems for mechanical systems is proposed. It is based on a direct discretization of the Lagrange-d’Alembert principle for the system (as opposed to using, for example, collocation or multiple shooting to enforce the equations of motion as constraints). The resulting forced discrete Euler-Lagrange equations then serve as constraints for the op...

In most books the Delaunay and Lagrange equations for the orbital elements are derived by the Hamilton-Jacobi method: one begins with the two-body Hamilton equations in spherical coordinates, performs a canonical transformation to the orbital elements, and obtains the Delaunay system. A standard trick is then used to generalise the approach to the N-body case. We re-examine this step and demons...

Reduction theory for mechanical systems with symmetry has its roots in the classical works in mechanics of Euler, Jacobi, Lagrange, Hamilton, Routh, Poincaré, and others. The modern vision of mechanics includes, besides the traditional mechanics of particles and rigid bodies, field theories such as electromagnetism, fluid mechanics, plasma physics, solid mechanics as well as quantum mechanics, ...

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...

In this paper an optimal control approach for thermal stress reduction inside a Czochralski grown single crystal is presented. Using the lateral heat flux as a control variable, an optimal control formulation for minimizing thermal stress with a given crystal shape is derived. Since thermal stress is also affected by the lateral shape of crystals during growth, the level of the stress can be re...

We derive the Euler-Lagrange equations for nonlinear elastic rods with self-contact. The excluded volume constraint is formulated in terms of an upper bound on the global curvature of the centreline. This condition is shown to guarantee the global injectivity of the deformation mapping of the elastic rod. Topological constraints such as a prescribed knot and link class to model knotting and sup...