Editing Classical Mechanics (section)

== <span style="color: #FFFFFF;">Analyzing</span> ==
{| class="wikitable"
|+ Newton vs. Lagrange vs. Hamilton
! Feature !! Newtonian (Forces) !! Lagrangian (Energy Difference) !! Hamiltonian (Total Energy)
|-
| Basic Variable || Force (F) || Potential (V) & Kinetic (T) || Position (q) & Momentum (p)
|-
| Perspective || "Pushing and Pulling" || "The Path of Least Action" || "Flow through Phase Space"
|-
| Usage || Rockets / Cars / Simple Physics || Robotics / Engines / Complex Links || Quantum Physics / Statistical Mech
|-
| Analogy || A 'Wrestler' pushing || A 'Skier' finding the best route || A 'Fluid' flowing in a map
|}

'''The Concept of "Constraints"''': Analyzing "Forced Motion." If a ball is "Glued to a table," Newton has to calculate the "Normal Force" of the table constantly. The Lagrangian approach simply "Removes the Z-variable" and solves the problem in 2D, ignoring the forces that "Keep it on the table." This "Elegant Laziness" is why physicists love it.
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