On tidal energy in Newtonian two-body motion

Two-body relaxation in modified Newtonian dynamics

A naive extension to MOND of the standard computation of the two-body relaxation time t2b implies that t2b is comparable to the crossing time regardless of the number N of stars in the system. This computation is questionable in view of the non-linearity of MOND’s field equation. A non-standard approach to the calculation of t2b is developed that can be extended to MOND whenever discreteness no...

Energy for N–Body Motion in Two Dimensional Gravity

A general definition of energy is given, via the Nöther theorem, for the N–body problem in (1 + 1) dimensional gravity. Within a first–order Lagrangian framework, the density of energy of a solution relative to a background is identified with the superpotential of the theory. For specific applications we reproduce the expected Hamiltonian for the motion of N particles in a curved spacetime. Thi...

Three-body equations of motion in successive post-newtonian approximations

On the Two-dimensional Rotational Body of Maximal Newtonian Resistance

We investigate, by means of computer simulations, shapes of nonconvex bodies that maximize resistance to their motion through a rarefied medium, considering that bodies are moving forward and at the same time slowly rotating. A two-dimensional geometric shape that confers to the body a resistance very close to the theoretical supremum value is obtained, improving previous results.

Kinetic Energy Harvester for Body Motion

This paper reports the design, fabrication, and testing of a permanent-magnet energy harvester generator for body motion. The described generator was capable to extract up to 117μW of power from walking, employing a non-resonant rotational mechanism. The planar generator proposed is composed of a rotor having multiple NdFeB permanent magnet pole-pairs with an eccentric proof mass. The stator ha...