## Lorentz Transformation

Derivation of Lorentz transformation equations using orthogonal transformations Let us consider two uniformly moving frames of reference where origins coincides at $t=0$. let the source of light is fixed at unprimed frame of reference and emits a pulse of light. The observer fixed in the unprimed frame of reference will observe a spherical wave-front propagating with the speed of light $c$ , whose equation can … Continue reading Lorentz Transformation »

## Degree of freedom and constraints

Definition: – The minimum number of independent variables or co-ordinates required for specifying the position of a dynamical system consisting of one or more particle is called Degree of freedom.

## Total energy of earth in its circular orbit around the sun

Question :
Find out the total energy of earth in its circular orbit around the sun in terms of gravitational constant
Let R be the total distance between the earth and the sun. If

## Brachistochrone Problem

Question
If a particle falls from rest under the influence of gravity from higher to lower point in the minimum time, what is the curve that the particle will follow?
Solution
Suppose v is the speed of the particle along the curve, then in traversing ds portion of the curve time spent would be

## Equations of motion of coupled pendulum using the lagrangian method

Question
Obtain the equations of motion of coupled pendulum using the lagrangian method.
Solution
Consider a system of coupled pendulums as shown below in the figure