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The motion of a mechanical system can be defined as a path through its configuration space. Computing such a path has a computational complexity scaling exponentially with the dimensionality of the configuration space. We propose to reduce…
We study the dynamics of three elastic particles in a finite interval where two light particles are separated by a heavy ``piston''. The piston undergoes surprisingly complex motion that is oscillatory at short time scales but seemingly…
Monocular vision-based target motion estimation is a fundamental challenge in numerous applications. This work introduces a novel bearing-box approach that fully leverages modern 3D detection measurements that are widely available nowadays…
A Clifford Space is counted to be a tempting approach to unify both micro-physics and macro-physics simultaneously. Such a tendency may be found in the realm of replacing vectors with poly-vectors. Accordingly, the problem of motion becomes…
The three-body general problem is formulated as a problem of geodesic trajectories flows on the Riemannian manifold. It is proved that a curved space with local coordinate system allows to detect new hidden symmetries of the internal motion…
This paper discusses some of the physical properties of plane symmetric self-similar solutions of the first kind (i.e., homothetic solutions). We are interested in calculating the expansion, the acceleration, the rotation, the shear tensor,…
We describe theoretically the process of multi-beam reflection in a two-dimensional electron system with a lateral potential barrier. Due to spin-orbital interaction, the reflection process leads to the formation of three beams with…
Brownian motion near soft surfaces is a situation widely encountered in nanoscale and biological physics. However, a complete theoretical description is lacking to date. Here, we theoretically investigate the dynamics of a two-dimensional…
We analytically solve the constraints in General Relativity for two black holes with arbitrary momenta and spin up to third order in these parameters. We compute the location and geometry of the apparent horizon, which depend on the spins,…
Random motions on the line and on the plane with space-varying velocities are considered and analyzed in this paper. On the line we investigate symmetric and asymmetric telegraph processes with space-dependent velocities and we are able to…
We derive a semi-geostrophic variational balance model for the three-dimensional Euler--Boussinesq equations on the non-traditional $f$-plane under the rigid lid approximation. The model is obtained by a small Rossby number expansion in the…
This article solves an optimal control problem arising in attitude control of a spacecraft under state and control constraints. We first derive the discrete-time attitude dynamics by employing discrete mechanics. The orientation transfer,…
This research investigates the rotational dynamics of a charged axisymmetric spinning rigid body influenced by gyrostatic torque. The study also accounts for the effects of transverse and constant body-fixed torques and an electromagnetic…
The derivation of the equation of one-dimensional movement of a solitary shock wave is given. This derivation shows, that the differential equation of movement of a solitary plane shock wave in the channel with variable area, is exact, if…
This paper proposes a methodology to stabilize relative equilibria in a model of identical, steered particles moving in three-dimensional Euclidean space. Exploiting the Lie group structure of the resulting dynamical system, the…
Equation for anomalous diffusion in momentum space, recently obtained in the recent paper (S.A. Trigger, ArXiv 0907.2793 v1, [cond-matt. stat.-mech.], 16 July 2009) is solved for the stationary and non-stationary cases on basis of the…
Piecewise constant curvature is a popular kinematics framework for continuum robots. Computing the model parameters from the desired end pose, known as the inverse kinematics problem, is fundamental in manipulation, tracking and planning…
Automatically generating agile whole-body motions for legged and humanoid robots remains a fundamental challenge in robotics. While numerous trajectory optimization approaches have been proposed, there is no clear guideline on how the…
The trajectory of a spherical object which falls freely in a gravitational field is fixed by its initial position and velocity. However, an object which can control its shape can also control its motion: Except where forbidden by symmetries…
For a spin-1/2 particle moving in a background magnetic field in noncommutative phase space, Dirac equation is solved when the particle is allowed to move off the plane that the magnetic field is perpendicular to. It is shown that the…