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In classical physics and special relativity, an inertial frame of reference (also called an inertial space or a Galilean reference frame) is a frame of reference in which objects exhibit inertia: they remain at rest or in uniform motion relative to the frame until acted upon by external forces. In such a frame the laws of nature can be observed ...
An observational frame (such as an inertial frame or non-inertial frame of reference) is a physical concept related to state of motion. A coordinate system is a mathematical concept, amounting to a choice of language used to describe observations. [3]
The center of momentum frame is defined as the inertial frame in which the sum of the linear momenta of all particles is equal to 0. Let S denote the laboratory reference system and S′ denote the center-of-momentum reference frame. Using a Galilean transformation, the particle velocity in S′ is
The Earth frame is also useful in that, under certain assumptions, it can be approximated as inertial. Additionally, one force acting on the aircraft, weight, is fixed in the +z E direction. The body frame is often of interest because the origin and the axes remain fixed relative to the aircraft.
Inertia is the natural tendency of objects in motion to stay in motion and objects at rest to stay at rest, unless a force causes the velocity to change. It is one of the fundamental principles in classical physics, and described by Isaac Newton in his first law of motion (also known as The Principle of Inertia). [1]
In the inertial frame, the differential equation is not always helpful in solving for the motion of a general rotating rigid body, as both I in and ω can change during the motion. One may instead change to a coordinate frame fixed in the rotating body, in which the moment of inertia tensor is constant.
The universe, as represented by the average motion of distant galaxies, does not appear to rotate relative to local inertial frames. Newton's gravitational constant G is a dynamical field. An isolated body in otherwise empty space has no inertia. Local inertial frames are affected by the cosmic motion and distribution of matter.
Let the coordinate system (x 1, x 2, x 3) be an inertial frame of reference, r be the position vector of a point particle in the continuous body with respect to the origin of the coordinate system, and v = dr / dt be the velocity vector of that point.