Constraints and Lagrangian Dynamics by Dr. Yogesh Sonvane, Assistant Professor, Department of Applied Physics, Sardar Vallabhbhai National Institute of Technology, Surat I hope it helps my peers to get good marks in SY Mechanical Engineering. Constraints › Discussion up to now  All mechanics is reduced to solving a set of simultaneous, coupled, 2 nd order differential equations which come from Newton’s 2 nd Law applied to each mass individually: (dpi/dt) = mi (d2 ri/dt2 ) = Fi (e) + ∑jFji  Given forces & initial conditions, the problem is reduced to pure math! › Oversimplification!! Many systems have CONSTRAINTS which limits their motion. – Example: Rigid Body. Constraints keep rij = constant. – Example: Particle motion on the surface of a sphere

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