相关论文: A "barbell" in a central force field: A case study…

We given an elementary illustration of symmetry reduction for central force problems, drawing phase portraits of the reduced dynamics as the intersection of Casimir and energy level sets in three dimensions. These systems form a classic…

Using variational minimizing methods,we prove the existence of an odd symmetric parabolic orbit for the 2-fixed center problems with weak force type homogeneous potentials.

In this paper we consider the central force problem in the special theory of relativity. We derive the special relativistic version of the Binet equation describing the orbit of a body. Then, the motion of a planet in a solar-like system…

In a central force system the apsidal angle is the angle at the centre of force between two consecutive apsis and measures the precession rate of the line of apsis. The apsidal angle has applications in different fields and the Newton's…

We study the motion of a particle in the hyperbolic plane (embedded in Minkowski space), under the action of a potential that depends only on one variable. This problem is the analogous to the spherical pendulum in a unidirectional force…

The reduction of dynamical systems has a rich history, with many important applications related to stability, control and verification. Reduction of nonlinear systems is typically performed in an exact manner - as is the case with…

NVIDIA researchers have pioneered an explicit method, position-based dynamics (PBD), for simulating systems with contact forces, gaining widespread use in computer graphics and animation. While the method yields visually compelling…

The aim of the present paper is to study the dynamics of a dumbbell satellite moving in a gravity field generated by an oblate body considering the effect of the zonal harmonic parameter. We prove that the pass trajectory of the mass center…

We study a mechanism of symmetry reduction in a higher-dimensional field theory upon orbifold compactification. Split multiplets appear unless all components in a multiplet of a symmetry group have a common parity on an orbifold. A gauge…

Nonholonomic mechanical systems have been attracting more interest in recent years because of their rich geometric properties and their applications in Engineering. In all generality, we discuss the reduction of a Hamilton-Jacobi theory for…

This contribution compiles the benefits of lattice symmetry in the context of closed orbit correction. A symmetric arrangement of BPMs and correctors results in structured orbit response matrices of Circulant or block Circulant type. These…

The paper is concerned with the development of efficient and accurate solution procedures for the isogeometric boundary element method (BEM) when applied to problems that contain inclusions that have elastic properties different to the…

This paper concerns the behaviour of the apsidal angle for orbits of central force system with homogenous potential of degree $-2\leq \alpha\leq 1$ and logarithmic potential. We derive a formula for the apsidal angle as a fixed-end points…

For For a given PDE system, or an exterior differential system possessing a Lie group of internal symmetries the orbit reduction procedure is introduced. It is proved that the solutions of the reduced exterior differential system are in…

We introduce a compactification of the group of rigid motions in 3-space derived from the Study model for this group. We use this compactifi-cation in robot kinematics, by considering the boundary of the configuration space of a robot. We…

In this note we will consider reduction techniques for Hamiltonian systems that are invariant under the action of a compact Lie group $G$ acting by symplectic diffeomorphisms, and the related work on stability of relative equilibria. We…

Lie-symmetry methods are used to determine the symmetry group of reduced magnetohydrodynamics. This group allows for arbitrary, continuous transformations of the fields themselves, along with space-time transformations. The derivation…

This paper explores how to adapt a new dynamical core to enable its use in one-way nested regional weather and climate models, where lateral boundary conditions (LBCs) are provided by a lower-resolution driving model. The dynamical core has…

The position-based dynamics (PBD) algorithm is a popular and versatile technique for real-time simulation of deformable bodies, but is only applicable to forces that can be expressed as linearly compliant constraints. In this work, we…

This paper presents methodologies for ensuring forward invariance of sublevel sets of constraint functions with high-relative-degree with respect to the system dynamics and in the presence of input constraints. We show that such constraint…