Notes Small oscillations Lagrangian approach is suitable for the system with small oscillation about an equilibrium position. The theory of small oscillation about equilibrium position is applicable in molecular spectra, …

Notes Introduction to continuous systems and fields Certain mechanical issues require a continuous system. For instance, consider the issue of an elastic solid that is vibrating. Here, the oscillation is caused by each point of the continuous ...

Notes Condition for steady Precession of Heavy Symmetrical top with one point fixed Consider the motion of a heavy symmetrical top spinning about the axis of symmetry, viz z'axis. The top is subject to a gravitational torque and is locked at its lower ...

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 ...