We present a method to enlarge the phase space of a canonical Hamiltonian System in order to remove coordinate singularities arising from a nontrivial topology of the configuration space. This “inflation” preserves the canonical structure of the system and generates new constants of motion that realize the constraints. As a first illustrative example the spherical pendulum is inflated by embedd...

Starting from the tri-Hamiltonian formulation of the Lagrange top in a six-dimensional phase space, we discuss the possible reductions of the Poisson tensors, the vector field and its Hamiltonian functions on a four-dimensional space. We show that the vector field of the Lagrange top possesses, on the reduced phase space, a quasibi-Hamiltonian formulation, which provides a set of separation var...

Robotics and autonomous systems have been instrumental to space exploration by enabling scientific breakthroughs and by fulfilling human curiosity and ambition to conquer new worlds. We provide an overview of space robotics as a rapidly emerging field, covering basic concepts, definitions, historical context, and evolution. We further present a technical road map of the field for the coming dec...

an analytical solution is presented for displacements and stresses of a three dimensional linear hyperelastic transversely isotropic layer bonded on the top of a transversely isotropic half-space subjected to an arbitrary, time-harmonic surface tangential force. the equations of equilibrium in terms of displacements are uncoupled by using a set of two potential functions introduced by eskandari...

Motivated by the necessity of a high-quality stray light control in detection gravitational waves space, spot size flat top beam generated clipping Gaussian (GB) is studied. By adopting mode expansion method (MEM) approach to simulating beam, slight variant definition mean square deviation (MSD) for MEM proposed. This enables us quickly estimate arbitrary propagation distances. Given that degre...

The Seifert-van Kampen Theorem involves the category Top∗ of spaces with base-point, the category Group of groups and the fundamental group functor π1 : Top∗ → Group; the theorem asserts that the functor π1 preserves certain special colimits. The generalisation of this theorem to all dimensions thus requires answers to three immediate questions, namely, what are the appropriate generalisations ...