Abstract
A detailed study is made of the Newtonian concept of force which is explicit in the first -Law of Motion. It is shown that for bodies of variable mass, where the total rate of change of momentum is not equal to the mass x acceleration of the body, the measurable nett force is given not by the total rate of change of momentum, but by the mass x acceleration of the body. A consistent theory of mechanics of variable masses is worked out using this definition of force and the various quantities involved are given clear and precise physical interpretation. These Newtonian ideas are then used to construct a theory of mechanics of variable rest-masses, within the frame-work of the Special Theory of Relativity. The relativistic -4-force is defined as the rest-mass x 4-acceleration and the theory of mechanics based on this definition is found to be consistent and. free of the discrepancies which previous theories of mechanics have suffered. Forces acting on large bodies are examined and the nature of such problems is formulated. The condition for the equilibrium of large bodies are discussed and illustrated by means of a well known problem. A detailed study is made of the concept of rest-mass as a preliminary to a description of continuum mechanics of variable rest-masses. The forms of energy which constitute the rest-mass of ponderable matter are listed and discussed in a general way. A continuum mechanics of variable rest-mass media is then constructed using the definition of force as rest-mass x 4-acceleration. The concept of the energy-momentum tensor is discussed and the rules for the decomposition of the total energy-momentum tensor into two physically meaningful tensors ( energy-momentum tensor of ponderable matter and the energy-momentum tensor of reaction) are laid out. The method of calculating the energy-momentum tensor of reaction is discussed and a Theorem of Virtual Power is derived. The use of the theorem is demonstrated by first applying it to simple material continua. Finally the revised theory of mechanics is applied to an electromagnetic material medium. The energy-momentum tensor of reaction is derived using the Theorem of Virtual Power and using this tensor, a detailed description of the energy, momentum and force distributions in the material medium is given.