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.
Holonomic constraints are those that can be expressed in the form of equations involving the ______ _______ _______ _____ _____ _______ _______ ________ _______ __________ ________ _______.
______ _____ _______ ______ ______.
____ __________ ____ ________ __________.
____ ______ __________ _________ ________ ______ ______ ________ _________ _______ ___.
________ ___ ______ ______ ________ __________ _________.
______ ___ _____ _________ ___ _________.
_______ _____ _____ ________ _____ _____ _____ ________.
_____ _____ _________ __________ ___ ____ ___ ______ _____.
_________ __________ _____ _________ _____ ________ __________ ____ _____ ________ _____ ___.
_________ _______ ____ ___ ________ _______ _____ _____ __________ ______.
______ ______ __________ _______ _______ ____ ________ ______.
__________ _____ ________ ______ ____ ______ _________ __________.
___ ____ ____ __________ _______ __________.
_________ _______ __________ ____ _____ ___ ________ _________ _________.
________ __________ _______ __________ ________ ________ _____ _____ __________ _________ ______.
________ _____ ____ _________ __________ ______ _______ __________.
___ _______ _______ ___ ___ _______ ___ _____ ________ _____ _________.
___ ______ _________ ________ _________ ________.
___ ____ _____ ________ ______ ____.
________ ________ _________ ______ _____ _______ ________ __________.
____ ___ _____ ________ ________ _________ ________ ___ ___ ________ ____ ______.
________ ____ _____ __________ _________ _____ ________.
____ _____ __________ __________ __________ __________.
_______ ______ ______ _________ ___ ____ _________ ___ ____ ________ _______.
Get Full Answer on WhatsApp
Derive the Euler-Lagrange equation of motion for a bead of mass m sliding due to gravity on a circular wire.
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 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.
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 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.
Explain whether the displacement is stable or unstable for the two cases.
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 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