Particle sliding off a sphere, using Lagrangian mechanics

Using Lagrangian mechanics and Lagrange multipliers to find the angle at which a particle sliding off a sphere from rest loses contact with the surface. Some other relevant videos are linked below!

Understanding Lagrange multipliers:    • Constrained Lagrangian mechanics: und...  

Solving the same problem (but with arbitrary initial velocity) using Newtonian mechanics:    • Particle sliding down a sphere: when ...  

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