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Gravitational systems in astrophysics often comprise a body -- the primary -- that far outweights the others, and which is taken as the centre of the reference frame. A fictitious acceleration, also known as the indirect term, must…

Transformation rules for coordinates, velocities and accelerations in accelerated reference frames are derived. A generalized approach of the special relativity is taken for a basis. A 7-dimensional space including projections of velocity…

Establishing the existence of periodic orbits is one of the crucial and most intricate topics in the study of dynamical systems, and over the years, many methods have been developed to this end. On the other hand, finding closed orbits in…

Lightsails are a promising spacecraft concept that can reach relativistic speeds via propulsion by laser light, allowing travel to nearby stars within a human lifetime. The success of a lightsail mission requires that any motion in the…

Relative motions have long been known to mislead the unsuspecting observers to false interpretations of reality. The deceptions are usually brief and unimportant, though relative motions have also led to illusions that were both…

In the Special Theory of Relativity space and time intervals are different in different frames of reference. As a consequence, the quantity 'velocity' of classical mechanics splits into different quantities in Special Relativity, coordinate…

Rotations and poses are ubiquitous throughout many fields of science and engineering such as robotics, aerospace, computer vision and graphics. In this paper, we provide a complete characterization of rotations and poses in terms of the…

We introduce and analyze a model for the dynamics of flocking and steering of a finite number of agents. In this model, each agent's acceleration consists of flocking and steering components. The flocking component is a generalization of…

The dynamics of systems of multiple gravitationally interacting bodies is often studied in a frame attached to one of the objects (e.g. a central star in a planetary system). As this frame is generally non-inertial, indirect forces appear…

A submarine moving at relativistic horizontal velocity sinks in Earth's rest frame due to length contraction while appearing to float in its own frame. Using spacetime geometry and the Lorentz transformations, we show that the resolution…

In analysing fluid forces on a moving body, a natural approach is to seek a component due to viscosity and an `inviscid' remainder. It is also attractive to decompose the velocity field into irrotational and rotational parts, and apportion…

This article handles in a short manner a few Laplace transform pairs and some extensions to the basic equations are developed. They can be applied to a wide variety of functions in order to find the Laplace transform or its inverse when…

Two complementary and equally important approaches to relativistic physics are explained. One is the standard approach, and the other is based on a study of the flows of an underlying physical substratum. Previous results concerning the…

On the bases of the Papapetrou equations with various supplementary conditions and other approaches a comparative analysis of the equations of motion of rotating bodies in general relativity is made. The motion of a body with vertical spin…

We consider a simple model of an internally driven self-rotating object; a rotor, confined to two dimensions by a thin film of low Reynolds number fluid. We undertake a detailed study of the hydrodynamic interactions between a pair of…

A general theory of frames of reference proposed in a preceding publication is considered here in the framework of the post-Newtonian approximation, assuming that the frame of reference is centered on a time-like geodesic. The problem of…

This paper proposes a new factor rotation for the context of functional principal components analysis. This rotation seeks to re-represent a functional subspace in terms of directions of decreasing smoothness as represented by a generalized…

This paper focuses on rotational phenomena of rigid body kinematics. It discusses them in a group-theoretic approach as completely as possible, using methods and notations as intuitive as possible. With a review of current literature, this…

Periodic orbits and cycles, respectively, play a significant role in discrete- and continuous-time dynamical systems (i.e. maps and flows). To succinctly describe their shifts when the system is applied perturbation, the notions of…

We give a simple and self contained introduction to quaternions and their practical usage in dynamics. The rigid body dynamics are presented in full details. In the appendix, some more exotic relations are given that allow to write more…