Can any body explain in simple and easy words "Lagrange Multiplier" What is it? and when it is used? i googled it but that was explained in much difficult words.
Isn't it similar to Lagrange equation of motions?The Lagrange multiplier is a additional auxiliary variable that appears when applying Lagrange's technique to solve an optimization problem with equality constraints by converting it to an unconstrained optimization problem. So: You get rid of the constraint at the cost of introducing an extra unknown.
To proceed, I think it is necessary to introduce notation for the function to be maximized (or: minimized) as well as the constraint(s). For this I could recommend the Wikipedia article, which seems quite accessible if you are familiar with some basic multivariable calculus.
Lagrange's formulation of classical mechanics is indeed based on a constrained energy minimization problem (where the constraints are dictated by the system's geometry) and the equations of motion are obtained from the "Lagrangian". The Lagrangian also appears more generally in constrained optimization problems, also in unrelated fields such as economics, but of course there it has another role and interpretation.Isn't it similar to Lagrange equation of motions?