62 citations · 216 across the 20 of their papers we have counts for
6 papers · 1 filter
The determination of the apsidal angles and Bertrand's theorem
Filadelfo C. Santos, Vitorvani Soares, Alexandre C. Tort
We derive an expression for the determination of the apsidal angles that holds good for arbitrary central potentials. Then we discuss under what conditions the apsidal angles remai…
An English translation o Bertrand's theorem
F. C. Santos, V. Soares, A. C. Tort
A beautiful theorem due to J. L. F. Bertrand concerning the laws of attraction that admit bounded closed orbits for arbitrarily chosen initial conditions is translated from French…
A non-perturbative proof of Bertrand's theorem
F C Santos, V Soares, A C Tort
We discuss an alternative non-perturbative proof of Bertrand's theorem that leads in a concise way directly to the two allowed fields: the newtonian and the isotropic harmonic osci…
The motion of two masses coupled to a massive spring
F C Santos, Y A Coutinho, L Ribeiro-Pinto +1
We discuss the classical motion of a spring of arbitrary mass coupled to two arbitrary massive blocks attached at its ends. A general approach to the problem is presented and some…
Remarks on the conservation of mechanical energy in introductory mechanics
F C Santos, V Soares, A C Tort
We discuss the work-kinetic energy theorem and the mechanical energy conservation theorem in the context of general physics courses. The motivation is the fact that all modern text…
Vector constants of motion for time-dependent Kepler and isotropic harmonic oscillator potentials
O. M. Ritter, F. C. Santos, A. C. Tort
A method of obtaining vector constants of motion for time-independent as well as time-dependent central fields is discussed. Some well-established results are rederived in this alt…