We will find a constant of motion with energy units for a relativistic particle moving in a quadratic dissipative medium subjected to a force which depends on the position. Then, we will find the Lagrangian and the Ha...We will find a constant of motion with energy units for a relativistic particle moving in a quadratic dissipative medium subjected to a force which depends on the position. Then, we will find the Lagrangian and the Hamiltonian of the equation of motion in a time interval such that the velocity does not change its sign. Finally, we will see that the Lagrangian and Hamiltonian have some problems.展开更多
In the first part of this paper, we found a more convenient algorithm for solving the equation of motion of a system of n bodies. This algorithm consists in solving first the trajectory equation and then the temporal ...In the first part of this paper, we found a more convenient algorithm for solving the equation of motion of a system of n bodies. This algorithm consists in solving first the trajectory equation and then the temporal equation. In this occasion, we will introduce a new way to solve the temporal equation by curving the horizontal axis (the time axis). In this way, we will be able to see the period of some periodic systems as the length of a certain curve and this will allow us to approximate the period in a different way. We will also be able to solve some problems like the pendulum one without using elliptic integrals. Finally, we will solve Kepler’s problem using all the formalism.展开更多
This paper has two parts, in this occasion we will present the first one. Until today, there are two formulations of classical mechanics. The first one is based on the Newton’s laws and the second one is based on the...This paper has two parts, in this occasion we will present the first one. Until today, there are two formulations of classical mechanics. The first one is based on the Newton’s laws and the second one is based on the principle of least action. In this paper, we will find a third formulation that is totally different and has some advantages in comparison with the other two formulations.展开更多
文摘We will find a constant of motion with energy units for a relativistic particle moving in a quadratic dissipative medium subjected to a force which depends on the position. Then, we will find the Lagrangian and the Hamiltonian of the equation of motion in a time interval such that the velocity does not change its sign. Finally, we will see that the Lagrangian and Hamiltonian have some problems.
文摘In the first part of this paper, we found a more convenient algorithm for solving the equation of motion of a system of n bodies. This algorithm consists in solving first the trajectory equation and then the temporal equation. In this occasion, we will introduce a new way to solve the temporal equation by curving the horizontal axis (the time axis). In this way, we will be able to see the period of some periodic systems as the length of a certain curve and this will allow us to approximate the period in a different way. We will also be able to solve some problems like the pendulum one without using elliptic integrals. Finally, we will solve Kepler’s problem using all the formalism.
文摘This paper has two parts, in this occasion we will present the first one. Until today, there are two formulations of classical mechanics. The first one is based on the Newton’s laws and the second one is based on the principle of least action. In this paper, we will find a third formulation that is totally different and has some advantages in comparison with the other two formulations.
