Conservation of Mechanical Energy Proof (2DoF)

The video tutorial explains the conservation of mechanical energy in two dimensions, involving calculus concepts like the multivariable chain rule and gradients. It starts with defining the equation of motion for a particle under an external force and introduces potential energy as a scalar function. Through mathematical derivation, it proves that the sum of kinetic and potential energy remains constant, demonstrating energy conservation. The tutorial concludes by discussing the conditions under which this conservation holds, specifically when forces are conservative.

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