Can Newton's Method Solve Freer Motion?

[Juli]

Hello everyone,

my question is, if there is a case, where you can't you Langrange (1 or 2) but only Newton to solve the equation of motion?
My guess is, that it might be, when we have no restrictions at all, so a totally free motion.
Does anybody know?

 

[Orodruin]

What do you mean by Lagrange 1 and 2? That does not seem like standard nomenclature to me. Please be specific.

Generally, the equations of motion are differential equations and whether they can be solved or not does not depend on the theory you used to derive them. Where you could fail is in arriving at a set of equations of motion.

 

[vanhees71]

Usually "Lagrange 1" is the formulation with the (holonomic) constraints treated with Lagrange multipliers, while "Lagrange 2" is the formulation in terms of an appropriate set of "generalized coordinates".

 

[Orodruin]

Regardless, it should probably be pointed out that Lagrange mechanics is perfectly applicable to systems without constraints. It could even be argued it does better in ease of deriving constants of motion etc. Where you can run into issues is when there are dissipative forces (eg, friction) acting on the system.