Classical mechanics

Question 1

How were we led to the Lagrangian formulation?

Answer 1

By the desire to eliminate the forces of constraint from the equations of motion.

Question 2

Write any additional benefit we got from forming the Lagrangian formula besides the goal.

Answer 2

We only have to deal with two scalar quantities, T and V in the Lagrangian formulation, whereas,
in the previous original Newton’s formulation, vectors like velocity and acceleration were involved.