In finding dynamic motion of particles we use laws of conservation of energy and momentum.
It is found the dynamics formulation using action integral
$$ \int (T-V)\, dt $$
builds ODEs for dynamic easily and quickly. I wondered why it could not have been taught along with the two (energy/momentum) invariant applications in classes parallel or succeeding undergraduate calculus. It is given a high aura if I may so say, made available in later classes only or in post graduation.
Spherical pendulum, planetary motion, motion of gravity fall with constraint etc. can be treated using Hamilton Least action principle conveniently. After learning to calculate natural frequencies for several systems the student need not wait for so long to apply in simple 3D formulations using the Euler- Lagrange equation from variational calculus. Just a suggestion.