Notes Heavy symmetrical top with one point fixed We can select a particular set of body axes such that the off-diagonal elements vanish and the expression of inertia only contains the diagonal elements. These axes are known as ...
Notes Rigid bodies- Kinematics and Dynamics The independent coordinates of a rigid bodyConsider a rigid body with three non-collinear points p, q, and r. Since each particle has three degrees of freedom, a total of ...
Notes Type of the canonical transformation generated by W Consider a canonical transformation in which the new momenta pj are all constants of the motion α in particular is the constant of motion H, i.e., H(qj,pj)= α . Taking ...
Notes Angular momentum and Kinetic energy of motion about a point Angular momentum is a measure of the rotational motion of an object around an axis or a point. It is defined as the product of the moment of inertia (a ...
Notes Effect of coriolis force on a projectile shot along the earth's surface Let P represent a location on the earth's surface at latitude λ. Take into account a rectangular Cartesian coordinate system with P as the swiftly fixed origin. The system's z ...
Notes Equation of motion of a spherical pendulum using Lagrange's equation of motion. A pendulum in which bob is constrained to move on a sphere rather than on a circle is called spherical pendulum. The position of the bob is located by spherical ...
Notes Lagrangian for a simple pendulum and equation describing its motion The angle θ between rest position and deflected position is chosen as generalized coordinate. If the string is of length l, then kinetic energy iswhere m is the ...
Notes D'Alembert's principle Consider a system in equilibrium, i.e. total force Fi on every particle is zero. Then work done by this force in a small virtual displacement δr will also vanish i.e., ...
