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...See more
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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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