"In physics, a Galilean transformation is used to transform between the coordinates of two reference frames which differ only by constant relative motion within the constructs of Newtonian physics."
A mathematical method for transforming between different reference frames.
Frame of Reference: A set of coordinates used to specify the position of a point in space-time.
Galilean Transformation: The equations used to transform the coordinates of an event from one frame of reference to another that is moving at a constant velocity relative to the first.
Relative Velocity: The velocity of an object with respect to another object or a frame of reference.
Time Dilation: The phenomenon in which the time interval between two events is longer in the frame of reference moving at a higher velocity.
Length Contraction: The phenomenon in which an object appears shorter in length in the frame of reference moving at a higher velocity.
Lorentz Factor: A scalar factor that appears in the equations of special relativity and is related to time dilation and length contraction.
Velocity Addition: The manner in which velocities are combined when observed from different frames of reference.
Kinematic Equations: A set of equations used to describe the motion of an object in one or more dimensions.
Inertial Frame of Reference: A frame of reference in which the laws of physics are observed to hold true under all conditions of constant velocity.
Non-inertial Frame of Reference: A frame of reference in which the laws of physics are not observed to hold true due to the effects of acceleration or rotation.
Translation: This type of transformation represents a change in position without any change in direction or orientation. It is a simple shift in the coordinates of the object's position.
Rotation: This type of transformation describes a change in orientation, where the object is rotated about some axis. The object's position in space remains the same, but its velocity and acceleration change.
Velocity Transformation: This type of transformation considers the change in velocity of the object as viewed from different frames of reference. It takes into account how the velocity of the observer affects the observed velocity of the object.
Inertial Transformation: This type of transformation accounts for the acceleration of the observer's frame of reference. It considers how the acceleration of the observer affects the apparent acceleration of the object.
"These transformations together with spatial rotations and translations in space and time form the inhomogeneous Galilean group."
"Without the translations in space and time, the group is the homogeneous Galilean group."
"The Galilean group is the group of motions of Galilean relativity acting on the four dimensions of space and time, forming the Galilean geometry."
"In special relativity, the homogenous and inhomogenous Galilean transformations are, respectively, replaced by the Lorentz transformations and Poincaré transformations."
"The group contraction in the classical limit c → ∞ of Poincaré transformations yields Galilean transformations."
"The equations below are only physically valid in a Newtonian framework."
"Galileo formulated these concepts in his description of uniform motion."
"The topic was motivated by his description of the motion of a ball rolling down a ramp, by which he measured the numerical value for the acceleration of gravity near the surface of the Earth."
"Two reference frames differ only by constant relative motion within the constructs of Newtonian physics."
"The group of motions of Galilean relativity acts on the four dimensions of space and time."
"The homogenous and inhomogenous Galilean transformations are, respectively, replaced by the Lorentz transformations and Poincaré transformations."
"The group contraction in the classical limit c → ∞ of Poincaré transformations yields Galilean transformations."
"The equations below are only physically valid in a Newtonian framework."
"Galileo formulated these concepts in his description of uniform motion."
"By which he measured the numerical value for the acceleration of gravity near the surface of the Earth."
"The Galilean group is the group of motions of Galilean relativity acting on the four dimensions of space and time, forming the Galilean geometry."
"Not applicable to coordinate systems moving relative to each other at speeds approaching the speed of light."
"These transformations together with spatial rotations and translations in space and time form the inhomogeneous Galilean group."
"In special relativity, the homogenous and inhomogenous Galilean transformations are respectively replaced by the Lorentz transformations and Poincaré transformations."