A new basic object — point-body [1 - 5] is introduced into consideration (1994). It is assumed that the point-body occupies zero volume, and its motion is described completely by means of its radius-vector and its rotation (turn) tensor. It is postulated that the kinetic energy of a point-body is a quadratic form of its translational and angular velocities, and its momentum and proper kinetic moment (dynamic spin) are defined as partial derivatives of the kinetic energy with respect to the vector of translational velocity and the vector of angular velocity, respectively. It was considered (2003) the model of a point-body [5], whose structure is determined by three parameters: mass, inertia moment, and an additional parameter q, conventionally named charge, which never appeared in particles used in classical mechanics. It is shown that the motion of this particle by inertia in a void space has a spiral trajectory, and for some initial conditions — a circular trajectory. Thus it is shown that in an inertial frame reference the motion of an isolated particle (point-body) by inertia has not to follow necessarily a linear path.
There was developed (1994) a concept of actions [1 - 5]. This concept is based on an axiom which supplements the Galileo's Principle of Inertia, generalising it to the bodies of general kind. This axiom states that in an inertial system of reference an isolated closed body moves in such a way that its momentum and kinetic moment remain invariable. Further, the forces and torques are introduced into consideration, and the force acting upon a closed body is defined as a cause for the change of the momentum of this body, and the torque, acting upon a closed body — as a cause of the change of the kinetic moment. The couple of vectors — force vector and the couple vector — are called action.
The concept of the internal energy of a body, consisting of point-bodies of general kind [1 - 5], was developed (1994); the axioms for the internal energy to be satisfied are formulated. The principally new idea is to distinguish the additivity by mass and additivity by bodies. The kinetic energy of a body is additive by its mass. At the same time, the internal energy of a body is additive by sub-bodies of which the body under consideration consists of, but, generally speaking, it is not an additive function of mass. In the Cayley problem, the paradox, related to the loss of energy, is resolved [5].
Basic concepts of thermodynamics [4, 5]: internal energy, temperature, and entropy are introduced (2002) on elementary examples of mechanics of discrete systems. The definition of the temperature concepts and entropy are given by means of purely mechanical arguments, based on the use of a special mathematical formulation of the energy balance.