Applications to Mechanics

Question 1

principle of stationary action

Answer 1

the motion between two positions of a mechanical system is described by an extremal of the functional where L is given by KE-PE

Question 2

move under a holonomic constraint

Answer 2

its position variable satisfies an equation F(x1,…,xn)=0

Question 3

generalised coordinates

Answer 3

coordinates by KE-PE

Question 4

invariant Lagrangian under a transformation

Answer 4

equal under transformation

Question 5

Noether’s theorem

Answer 5

invariant Lagrangian under 1-parameter group of transformations X(s)
then every solution of EL satisfies the conservation law
<partial X wrt s, partial L wrt v>=constant