Are there other less famous yet accepted formalisms of Classical Mechanics? I was lately studying about the Lagrange and Hamiltonian Mechanics. This gave me a perspective of looking at classical mechanics different from that of Newton's. I would like to know if there are other accepted formalism of the same which are not quite useful compared to others (because otherwise if would have been famous and taught in colleges)?
 A: Gauss's principle of least constraint
Principles of Least Action and of Least Constraint (a review paper by E.Ramm)
If I remember correctly, this principle has been used to derive equations of motion
for Gaussian isokinetic thermostat (i.e., a computational algorithm for maintaining a fixed temperature of the system). Please see, for example, Statistical Mechanics of Nonequilibrium Liquids by Denis J. Evans and Gary P. Morriss, Sec.5.2.
Excerpt from the paper by E. Ramm above (in the last page):
Gauss’s Principle is not very well known although it is mentioned as a fundamental principle in many treatises, e. g. [3, 25–27], see also [28]; correspondingly it has not been applied too often. Evans and Morriss [26] discuss in detail the application of the Principle for holonomic (constraints depend only on co-ordinates) and nonholonomic constraints (non-integrable con- straints on velocity) and conclude ”The correct application of Gauss’s principle is limited to arbitrary holonomic constraints and apparently, to nonholonomic constraint functions which are homogeneous functions of the momenta”.
A: Kane's Method is another accepted formalism (Thomas R. Kane) which is a method for formulating equations of motion.
