The differential equations of motion deduced from the principle of minimal reaction
Abstract
Covic and Lukacevic (1985) have provided an interpretation of the Gauss principle of least constraint, taking into account the motion of a constrained system of N material points. The present paper is concerned with the derivation of the differential equations of motion for both the free and the constrained mechanical systems. It is found that, in the absence of active forces, the principle of minimal reaction reduces to the principle of minimal acceleration of the representative point (RP). Under certain conditions regarding the constraints, both the normal and the tangential accelerations separately have their minimum for the actual motion. It is pointed out that the minimality of the normal acceleration expresses the Hertz principle of the least curvature, whereas the minimality of the tangential acceleration leads to the law of the conservation of energy.
 Publication:

Gesellschaft angewandte Mathematik und Mechanik Jahrestagung Goettingen West Germany Zeitschrift Flugwissenschaften
 Pub Date:
 1986
 Bibcode:
 1986GMMWJ..66..379L
 Keywords:

 Differential Equations;
 Equations Of Motion;
 Gauss Equation;
 Theoretical Physics;
 Acceleration (Physics);
 Curvature;
 Physics (General)