What are holonomic and non- holonomic constraints ? Write down the equations for the constraints for three point masses connected by rigid rods of length L.
In Classical Mechanics-I, constraints are conditions that restrict the motion of a system. Constraints can be classified into holonomic and non-holonomic types based on whether they can be expressed as equations relating coordinates and time.
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Consider a potential V (r) = kr2 , k > 0.
(i) Obtain the expression for effective potential Veff (r) .
(ii) Determine the nature of the force associated with the potential.
(iii) Obtain rmin and for a two-body system.
(iv) Show that the Laplace-Runge-Lenz vector is not conserved for the given potential.
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A mass on the end of a spring, has a natural frequency 2ω , The system is immersed in a fluid that causes the motion to be overdamped, Γ = -bq . Obtain the times at which the speed of the mass becomes maximum
What are holonomic and non- holonomic constraints ? Write down the equations for the constraints for three point masses connected by rigid rods of length L.
Consider a spring mass pendulum, where m is the mass of the pendulum. The motion of the pendulum is constrained as given in the figure:
The motion is assume to take place only in the vertical plane. The equilibrium length of the spring is l , while its angle with the vertical is θ(t) . Obtain the equations of motion for x and θ.
A bead of mass m slides on a smooth rod which is rotating about one fixed end in a vertical plane with uniform angular velocity ω .
Write the Lagrangian for the system and obtain the equation of motion.
Consider a system as given in the figure, where the masses M are fixed and m is the dynamical system:
(i) Write the change in potential for a small displacement.
(ii) Write the change in potential for a small perpendicular displacemen.
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