THE THIRD PRINCIPLE OF DYNAMICS
Author: Nicolae Mazilu
Published on Friday, March 21st, 2008 in category ProtoQuant
D’Alembert Principle
The Science is not at all unaccustomed with such “broadenings of a class” so to speak, which appeared even under the auspices of the Second Principle of Dynamics as given by equation (6) for forces. This is, for instance, the essence of D’Alembert Principle, at least in the form in which it has been enounced for the first time. Namely, from equation (6) we define the 1-form of attraction
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(15) |
Then the particle freedom is here expressed by
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(3”) |
where u is a conveniently chosen differential 1-form. Therefore we are here in the “class u”. If u is built, for instance, upon a displacement vector, then every material point, part of the material point whose particles are defined according to equation (3”), is characterized by the equation
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(16) |
where 
is the displacement vector. In cases where this vector can be taken as difference between positions we have in (16) the equation of a harmonic oscillator that gave Fresnel the right to describe the light by mechanical oscillations.