Without making recourse to Newton's law of gravitation and starting from the concept of gravitational force, the concepts of active gravitational mass and of passive gravitational mass are introduced. Furthermore it is proved that they can be identified and that in Newton's law of gravitation the linear dependence on masses necessarily follows from the principle of superposition of simultaneous forces and from Newton's third law of dynamics.
In the case of a satellite in a circular orbit the solutions of Euler's equations are not single-valued for arbitrary initial values.
The spherical version of the two-dimensional central harmonic oscillator, as well as the spherical Kepler (Schrödinger) potential, are superintegrable systems with quadratic constants of motion. They belong to two different spherical "Smorodinski-Winternitz" families of superintegrable potentials. A new superintegrable oscillator have been recently found in S². It represents the spherical version of the nonisotropic 2:1 oscillator and it also belongs to a spherical family of quadratic superintegrable...
In this work we determine for the Cattaneo heat propagation system all the supplementary balance laws (shortly SBL) of the same order (zero) as the system itself and extract the constitutive relations (expression for the internal energy) dictated by the Entropy Principle. The space of all supplementary balance laws (having the functional dimension 8) contains four original balance laws and their deformations depending on 4 functions of temperature (). The requirements of the II law of thermodynamics...
This paper presents a method for building a foothold selection module as well as methods for the stability check for a multi-legged walking robot. The foothold selection decision maker is shaped automatically, without expert knowledge. The robot learns how to select appropriate footholds by walking on rough terrain or by testing ground primitives. The gathered knowledge is then used to find a relation between slippages and the obtained local shape of the terrain, which is further employed to assess...
Dans cet article nous donnons les formes normales des sytèmes linéaires hamiltoniens antisymétriques accessibles . Nous construisons une stratification et une décomposition cellulaire analytique de , puis nous prouvons que son groupe d’homotopie est isomorphe à celui d’une grassmanienne. Ensuite, nous démontrons que est homotopiquement équivalent à l’espace des systèmes linéaires accessibles. En appliquant ces résultats topologiques, on peut prouver qu’il n’existe pas de paramétrisation continue...