The Lagrange multiplier technique provides a powerful, and elegant, way to handle holonomic constraints using Euler’s equations. The general method of Lagrange multipliers for n variables, with m ...The Lagrange multiplier technique provides a powerful, and elegant, way to handle holonomic constraints using Euler’s equations. The general method of Lagrange multipliers for n variables, with m constraints, is best introduced using Bernoulli’s ingenious exploitation of virtual infinitessimal displacements, which Lagrange signified by the symbol δ.
The state of the system at any time can be represented by a single point in 3N -dimensional space. However, in many systems, the particles may not be free to wander anywhere at will; they may be subj...The state of the system at any time can be represented by a single point in 3N -dimensional space. However, in many systems, the particles may not be free to wander anywhere at will; they may be subject to various constraints. A constraint that can be described by an equation relating the coordinates (and perhaps also the time) is called a holonomic constraint, and the equation that describes the constraint is a holonomic equation.
Consider only motions of the system for which the extended lengths of the two springs are equal and opposite such that the two masses always are equal distances from the center of the rod keeping the ...Consider only motions of the system for which the extended lengths of the two springs are equal and opposite such that the two masses always are equal distances from the center of the rod keeping the center of mass at the center of the rod.
