Periodic orbits in the restricted problem of three bodies in a three-dimensional coordinate system when the smaller primary is a triaxial rigid body

Abstract

In this paper, we have studied the equations of motion for the problem, which are regularised in the neighbourhood of one of the finite masses and the existence of periodic orbits in a three-dimensional coordinate system when μ = 0. Finally, it establishes the canonical set (l, L, g, G, h, H) and forms the basic general perturbation theory for the problem.

Precision algorithms in second-order fractional differential equations

“…It can be seen that the algorithm curve in this paper is the same as the result of the conventional PSE expansion approximation of the Tustin transform operator as a whole. This is almost the same as the curve obtained by the most direct and simple G-L definition discrete method [11]. The G-L method is almost identical to the theory obtained by applying the Cauchy definition to remove the area around t = 0 + .…”

“…u(t) can be formed by a certain function and its fractional derivative. Considering formula (6), formula (7), formula (9), and formula (11), the approximate value d a i y k of D ai y(t) can be obtained. We rewrite it as…”

A Kinematic Information Acquisition Model That Uses Digital Signals from an Inertial and Magnetic Motion Capture System

“…The information received from the motion capture system is the raw material for the motion description and its corresponding simulation in a 3D virtual environment, which is achieved from the representation of the orientation and position of a rigid body. A rigid body is a system of many particles that keep a constant distance while the body is in motion following a trajectory, where its position changes with a fixed point reference, also known as the absolute coordinate system [47,48]. The position of the body is determined with the aid of the P position vector (consisting of two coordinates in the two-dimensional plane or three coordinates in a three-dimensional plane), representing the position of a certain point on the object compared to the zero position of the reference system.…”

Second-kind symmetric periodic orbits for planar perturbed Kepler problems and applications

“…In celestial mechanics, one of the most well-known integrable model is the Kepler problem. There exist many other problems that are formulated as a perturbation of the Kepler problem in Cartesian coordinates (see [5,6,10,13] and references therein) or in rotating coordinates (see, e.g., [16,21,25,27]). Poincaré [28] considered the investigation of periodic solutions of the restricted three-body problem where, in particular, he classified the periodic orbits of second kind that are generated by the elliptic orbits of the planar Kepler problem (the first kind are generated by the circular orbits of the planar Kepler problem).…”