Abstract

Certain generalization of Maxwell equations was proposed in paper [1]. It implies total time derivatives instead of the partial ones. Partial solution of this system was found for the case of the fields induced by electric charges. Scalar product of electric fields created by different charges determines their interaction energy and vector product of their magnetic fields determines their interaction impulse. Having calculated interaction energy gradient we obtain interaction force as Huygens understood it and having calculated impulse total time derivative we obtain Newton?s interaction force. It turns out that these forces physical sense and their mathematical description essentially differ. Gradiental part depends on charges velocities product and is equal to zero if at least one of the charges is in rest. This part incorporates force formulas earlier proposed by Ampere, Whittaker and Lorentz. The last one is usually defined by interaction of a certain charge called test charge and fields induced by other charge. Actually it coincides with force formula proposed by Grassman earlier. Proposed formula in contrast to Lorentz one satisfies the third Newtonial law. The second Newtonian part of the force formula depends on differences product of the charges velocities and accelerations. Therefore it predicts interaction in particular between moving and standing charges in addition to Coulomb one. It contains items earlier proposed for force description by Gauss and Weber. As in the case of Lorentz force formula it adds items which make Gauss and Weber force symmetric. Certain part of this force is light velocity c2 inverse and a part of it is c3 inverse. Apparently these items are essential for electroweak interaction. This paper is devoted to similar investigation of gravitational forces created by moving masses. Corresponding fields are described by Maxwell type equations in which first time derivatives are changed for the second ones. One can say that Electricity is a field of velocities and gravity is a field of accelerations. Solutions of such a system are used to construct interaction energy and interaction impulse. Gradient of scalar product of corresponding gravitational fields and second time derivative of vector product of gravimagnetic fields turn to be accurate analogues of electrodynamic interaction. But here forces depend not only on velocities and accelerations but on third and fourth derivatives as well.