jason12345 said:Hi.
Is there a quick way of deriving the Galilean transformations from the Galilean composition formula for velocities?
Cheers.
The Galilean transformation from velocity composition is a mathematical formula that describes how velocities are combined in different reference frames according to Galileo's principle of relativity. It allows us to understand how an object's velocity appears to change when observed from different perspectives.
The Galilean transformation works by adding or subtracting velocities according to the relative motion between two reference frames. If an object is moving at a velocity of v with respect to one reference frame and at a velocity of u with respect to another reference frame, its velocity with respect to the second reference frame would be v + u or v - u, depending on the direction of motion.
The Galilean transformation is a classical formula that describes the relationship between velocities in different reference frames, while the Lorentz transformation is a relativistic formula that takes into account the effects of time dilation and length contraction at high speeds. The Lorentz transformation reduces to the Galilean transformation at low speeds.
The Galilean transformation assumes that time and space are absolute, which is not consistent with the principles of special relativity. At high speeds approaching the speed of light, time dilation and length contraction occur, making the Galilean transformation inaccurate.
The Galilean transformation has various applications in classical mechanics, such as calculating the trajectory of a projectile, understanding the Doppler effect, and predicting the motion of objects in different reference frames. It is also used in engineering and navigation systems to analyze the motion of objects in different frames of reference.