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