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It is shown that physical mechanics for pointlike bodies can be effectively modeled in terms of the action of transformation groups that act as symmetries of the solutions of systems of differential equations that describe the integrability…
A simple model based on the maximum energy that an athlete can produce in a small time interval is used to describe the high and long jump. Conservation of angular momentum is used to explain why an athlete should run horizontally to…
We present an analysis of the motion of a simple torsion pendulum and we describe how, with straightforward extensions to the usual basic dynamical model, we succeed in explaining some unexpected features we found in our data, like the…
We derive a simple consistency relation from the running of the tensor-to-scalar ratio. This new relation is first order in the slow-roll approximation. While for single field models we can obtain what can be found by using other…
A universal inequality that bounds the angular momentum of a body by the square of its size is presented and heuristic physical arguments are given to support it. We prove a version of this inequality, as consequence of Einstein equations,…
We show that during normal modes of an oscillatory system consisting of a hoop and a cylinder joining their centers by an ideal spring, its central mass does not remain at rest. This effect is due to the resultant external static friction…
In this thesis, multipole expansions of mass, momentum and stress density will be made for a body in Newtonian mechanics. Using these definitions; momentum, angular momentum, center of mass, force and torque are defined for $N$…
Dynamical topological solitons are studied in classical two-dimensional Heisenberg easy-axis ferromagnets. The properties of such solitons are treated both analytically in the continuum limit and numerically by spin dynamics simulations of…
Future developments of lighter, more compact and powerful motors-driven by environmental and sustainability considerations in the transportation industry-involve higher stresses, currents and electromagnetic fields. Strong couplings between…
The problem of motion for different test particles, charged and spinning objects of constant spinning tensor in different versions of bimetric theory of gravity is obtained by deriving their corresponding path and path deviation equations,…
Euler's equation relates the change in angular momentum of a rigid body to the applied torque. This paper fills a gap in the literature by using Lagrangian dynamics to derive Euler's equation in terms of generalized coordinates. This is…
The method of Morse theory is used to analyze the distributions of unit charges interacting through a repulsive force and constrained to move on the surface of a sphere -- the Thomson problem. We find that, due to topological reasons, the…
It is pointed out that the current form of extrinsic equation of motion for a particle constrained to remain on a hypersurface is in fact a half-finished version for it is established without regard to the fact that the particle can never…
The motion of a ruck in a rug is used as an analogy to explain the role of dislocations in the deformation of crystalline solids. We take the analogy literally and study the shape and motion of a bump, wrinkle or ruck in a thin sheet in…
How do test bodies move in scalar-tensor theories of gravitation? We provide an answer to this question on the basis of a unified multipolar scheme. In particular, we give the explicit equations of motion for pointlike, as well as spinning…
In this paper we consider cases of existence of invariant measure, additional first integrals, and Poisson structure in a problem of rigid body's rolling without sliding on plane and sphere. The problem of rigid body's motion on plane was…
We examine the entropic picture of Newton's second law for the case of circular motion. It is shown that one must make modifications to the derivation of F=ma due to a change in the effective Unruh temperature for circular motion. These…
Analyzing the motion of a roller coaster allows for an instructive introduction of various theoretical concepts in a concrete and enjoyable context. We start by modeling the roller coaster train as a point particle. We then develop more…
Euler's interpretation of Newton's gravity (NG) as Archimedes' thrust in a fluid ether is presented in some detail. Then a semi-heuristic mechanism for gravity, close to Euler's, is recalled and compared with the latter. None of these two…
Multi-mode expansions in computational quantum dynamics promise convergence toward exact results upon increasing the number of modes. Convergence is difficult to ascertain in practice due to the unfavourable scaling of required resources…