The Special Relativistic Mechanics
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We shall start with a short review of the prerelativistic mechanics of Newton, Lagrange, and Hamilton. For simplicity we restrict ourselves to systems of a single-point particle having (constant) mass m > 0. Let the parameterized motion curve be given by xα = X α(t), in the Euclidean space E3. Let the three components of the force vector be given by f α(t, x, v), which are functions of seven real variables. Here t stands for the time variable, x = (x1,x2, x3) are the spatial coordinates in a Cartesian coordinate system, and v = (v1, v2, v3) are the velocity variables.
KeywordsHomogeneous Function Canonical Equation Motion Curve Hamiltonian Mechanic Extended Phase Space
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