Related papers: A simple derivation of Kepler's laws without solvi…
We discuss two applications of Riccati equation to Newton's laws of motion. The first one is the motion of a particle under the influence of a power law central potential $V(r)=k r^{\epsilon}$. For zero total energy we show that the…
A description of the motion in noninertial reference frames by means of the inclusion of high time derivatives is studied. Incompleteness of the description of physical reality is a problem of any theory, both in quantum mechanics and…
Lorentz Transformations of Special Relativity are derived from two postulates: the first is the Principle of Relativity, while the postulate of invariance of the velocity of light, used in usual derivations, is replaced by a law of…
It is demonstrated that energy conservation allows for a straight derivation of Newtonian mechanics without an apriori definition of the concept of work. Furthermore it is shown that energy must be depicted as a function of position and…
It has been known for some time that a 3D incompressible Euler flow that has initially a barely smooth velocity field nonetheless has Lagrangian fluid particle trajectories that are analytic in time for at least a finite time (Ph. Serfati…
We start by formulating geometrically the Newton's law for a classical free particle in terms of Riemannian geometry, as pattern for subsequent developments. In fact, we use this scheme for further generalisation devoted to a constrained…
The formal derivation of Langevin equations (and, equivalently Fokker-Planck equations) with projection operator techniques of Mori, Zwanzig, Kawasaki and others apparently not has widely found its way into textbooks. It has been reproduced…
This is an annotated translation of E126 'De novo genere oscillationum', in which Euler derived for the first time, the differential equation of the (undamped) simple harmonic oscillator under harmonic excitation, namely, the motion of an…
We consider the problem of computing the Euler characteristic of an abstract simplicial complex given by its vertices and facets. We show that this problem is #P-complete and present two new practical algorithms for computing Euler…
The present author recently proposed and proved a relationship theorem between nonlinear polynomial equations and the corresponding Jacobian matrix. By using this theorem, this paper derives a Newton iterative formula without requiring the…
The principles of the special theory of relativity are extremely simple. A knowledge of the Pythagorean theorem and an ability to perform the simplest algebraic operations are sufficient to be conversant with the kinematics of the special…
In the classical one-dimensional solution of fluid dynamics equations all unknown functions depend only on time t and Cartesian coordinate x. Although fluid spreads in all directions (velocity vector has three components) the whole picture…
We introduce a data-driven method for learning the equations of motion of mechanical systems directly from position measurements, without requiring access to velocity data. This is particularly relevant in system identification tasks where…
Despite the fact that it has been known since the time of Heisenberg that quantum operators obey a quantum version of Newton's laws, students are often told that derivations of quantum mechanics must necessarily follow from the Hamiltonian…
The algebra of the relativistic composition of velocities is shown to be isomorphic to an algebraic loop defined on division algebras. This makes calculations in special relativity effortless and straightforward, unlike the standard…
We show that the transformation of relativistic velocities derived without using the Lorentz-Einstein transformation for the space-time coordinates of the same event and the fact that we can define the proper value of length, time interval,…
This paper establishes calculus upon two physical facts: (1) any average velocity is always between two instantaneous velocities, and (2) the motion of an object is determined once its velocity has been determined. It directly defines…
We construct a normal form suited to {\it fast driven systems}. We call so systems including actions ${\rm I}$, angles {$\psi$}, and one fast coordinate $y$, moving under the action of a vector--field $N$ depending only on ${\rm I}$ and $y$…
The paper is devoted to the motion of a body in a fluid under the influence of gravity and drag. Depending on the regime considered, the drag force can exhibit a linear, quadratic or even more general dependence on the velocity of the body…
Computer simulation of the time evolution in a classical system is a standard numerical method, used in numerous scientific articles in Natural Science. Almost all the simulations are performed by discrete Molecular Dynamics (MD). The…