Related papers: Remarks on Newton's Second Law for Variable Mass S…
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…
The analogy between dynamics and optics had a great influence on the development of the foundations of classical and quantum mechanics. We take this analogy one step further and investigate the validity of Fermat's principle in…
Application of Newton's ideas from "Principia" gives many new results in mechanics. Here we explore the question ``What form of extra force will maintain the magnitude of a vector constant of the motion while changing its direction?''
The dynamic world model and its linear perturbations were first studied in Einstein's gravity. In the system without pressure the relativistic equations coincide exactly with the later known ones in Newton's gravity. Here we prove that,…
We investigate the validity of the generalized second law of thermodynamics, in the cosmological scenario where dark energy interacts with both dark matter and radiation. Calculating separately the entropy variation for each fluid component…
Newton's constant is the least well-measured among the fundamental constants of Nature, and, indeed, its accurate measurement has long served an experimental challenge. Levitated mechanical systems are attracting growing attention for their…
We showed that various expressions of stress in different models of fluids and in different forms of applying Newton's Second Law can be chosen, however there is always one Newton's Second Law which restricts and provides flexibility in…
The main purpose of this paper is to seek a mechanical interpretation of gravitational phenomena. We suppose that the universe may be filled with a kind of fluid which may be called the $\Omega (0)$ substratum. Thus, the inverse-square law…
We investigate quantum effects in the evolution of general systems. For studying such temporal quantum phenomena, it is paramount to have a rigorous concept and profound understanding of the classical dynamics in such a system in the first…
We present general relativistic correction terms appearing in Newton's gravity to the second-order perturbations of cosmological fluids. In our previous work we have shown that to the second-order perturbations, the density and velocity…
This work investigates the validity of the generalized second law of thermodynamics in modified f(R) Horava-Lifshitz gravity proposed by Chaichian et al (2010) [Class. Quantum Grav. 27 (2010) 185021], which is invariant under…
Quantum buoyancy has been proposed as the mechanism protecting the generalized second law when an entropy--bearing object is slowly lowered towards a black hole and then dropped in. We point out that the original derivation of the buoyant…
Following the basic idea expressed in [1], we assume that for any particle or body with mass M its own time t depends on therelative change \frac{\Delta M}{M} of that mass. Based on this assumption, one discusses possible existence of a…
The present study is motivated by the study of reference [1], where the generalized second law of thermodynamics has been investigated for a flat FRW universe for two viable models of $f(T)$ gravity. In the present work, we have considered…
In this paper, we review the recently formulated quantum laws of motion and provide new observations. We also extend these laws to higher dimensions. By applying in two dimensions the obtained relations to charge submitted to an electric…
We solve a set of selected exercises on rotational motion requiring a mechanical and thermodynamical analysis. When non-conservative forces or thermal effects are present, a complete study must use the first law of thermodynamics together…
We relate Newton's Second Law with the Second Law of Thermodynamics through the analysis of a simple model introducing a dynamic pressure concept. From this analyses we can clarify some conceptual problems resulting from several concepts of…
It is shown that all generalized two--dimensional dilaton theories with arbitrary matter content (with a curvature independent coupling to gravity) do not only obey a first law of black hole mechanics (which follows from Wald's general…
We explain the solution of the following two problems: obtaining of Kepler's laws from Newton's laws (so called two bodies problem) and obtaining the fourth Newton's law (the formula for gravitation) as a corollary of Kepler's laws. This…
The interaction between two parts in a compound quantum system may be reconsidered more completely than before and some new understandings and conclusions different from current quantum mechanics are obtained, including the conservation law…