Related papers: A rational Rodrigues' formula to interpolate rotat…
The orientation of a rigid object can be described by a rotation that transforms it into a standard position. For a symmetrical object the rotation is known only up to multiplication by an element of the symmetry group. Such ambiguous…
Relativistic modelling of rotational motion of extended bodies represents one of the most complicated problems of Applied Relativity. The relativistic reference systems of IAU (2000) give a suitable theoretical framework for such a…
We derive a mathematical model for the motion of several insulating rigid bodies through an electrically conducting fluid. Starting from a universal model describing this phenomenon in generality, we elaborate (simplifying) physical…
In this article, we prove a generalized Rodrigues formula for a wide class of holonomic Laurent series, which yields a new linear independence criterion concerning their values at algebraic points. This generalization yields a new…
The rotation of the casing and rotor of a gyroscope is studied by considering frictional effects. Friction causes the casing to rotate, and over time, air dissipation and friction at the touchpoint gradually stop this rotation. Several…
It is fairly well known that rotation in three dimensions can be expressed as a quadratic in a skew symmetric matrix via the Euler-Rodrigues formula. A generalized Euler-Rodrigues polynomial of degree 2n in a skew symmetric generating…
Objects' rigid motions in 3D space are described by rotations and translations of a highly-correlated set of points, each with associated $x,y,z$ coordinates that real-valued networks consider as separate entities, losing information.…
We consider the problem of estimating the error when solving a system of differential algebraic equations. Richardson extrapolation is a classical technique that can be used to judge when computational errors are irrelevant and estimate the…
In this paper we introduce a family of rational approximations of the reciprocal of a $\phi$-function involved in the explicit solutions of certain linear differential equations, as well as in integration schemes evolving on manifolds. The…
Starting from the Rodrigues representation of polynomial solutions of the general hypergeometric-type differential equation complementary polynomials are constructed using a natural method. Among the key results is a generating function in…
A formula for the apparent rotation of a relativistically moving object has been known for some time, but it seems not to have been realized that this formula has a very pretty interpretation in terms of formal group laws. Version 2…
This preprint concerns a mathematically rigorous treatment of an interesting physical phenomenon in relativity theory. We would like to draw the reader's attention particularly to the abstract mathematical formalism of relativity (which was…
Rotation of a permanently polarized rigid body under the radiation reaction torque is considered. Dynamics of the spinning top is derived from a balance condition of the angular momentum. It leads to the non-integrable nonlinear 2nd-order…
The goals of this paper are to obtain theoretical models of what happens when a computer calculates the rotation set of a homeomorphism, and to find a good algorithm to perform simulations of this rotation set. To do that we introduce the…
This paper presents a novel approach to numerically describe the interactions between rigid bodies, with a special focus on robotic grasping. Some of the more common approaches used to address such issues rely on satisfaction of a set of…
Exact and simple calculation of Thomas rotation and Thomas precessions along a circular world line is presented in an absolute (coordinate-free) formulation of special relativity. Besides the simplicity of calculations the absolute…
We review the developments in modeling gravitational recoil from merging black-hole binaries and introduce a new set of 20 simulations to test our previously proposed empirical formula for the recoil. The configurations are chosen to…
A modified Gibbs's rotation matrix is derived and the connection with the Euler angles, quaternions, and Cayley$-$Klein parameters is established. As particular cases, the Rodrigues and Gibbs parameterizations of the rotation are obtained.…
This work is devoted to a systematic exposition of the dynamics of a rigid body, considered as a system with kinematic constraints. Having accepted the variational problem in accordance with this, we no longer need any additional postulates…
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…