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Symmetries and Group Theory
Published in Mattias Blennow, Mathematical Methods for Physics and Engineering, 2018
Already Newtonian mechanics has the notion of inertial frames built into it. An inertial frame is a frame of reference in which the laws of physics hold in their simplest form. For example, Newton’s laws hold as stated in all inertial frames. All inertial frames are related to each other by a fixed rotation and a linearly time dependent translation. As such, they move with constant velocity with respect to each other. An event is specified by giving a time and a point in space, i.e., it specifies when and where, and is described by four coordinates (t, x→) in space-time for any inertial frame.
A comparative study on electrocentrifuge spinning and electrospinning process as two different nanofiber creation techniques
Published in A. K. Haghi, Lionello Pogliani, Eduardo A. Castro, Devrim Balköse, Omari V. Mukbaniani, Chin Hua Chia, Applied Chemistry and Chemical Engineering, 2017
Centrifugal force is an outward force apparent in a rotating reference frame; it does not exist when measurements are made in an inertial frame of reference. All measurements of position and velocity must be made relative to some frame of reference. For example, if we are studying the motion of an object in an airliner traveling at great speed, we could calculate the motion of the object with respect to the interior of the airliner, or to the surface of the earth. An inertial frame of reference is one that is not accelerating (including rotation). The use of an inertial frame of reference, which will be the case for all elementary calculations, is often not explicitly stated but may generally be assumed unless stated otherwise.35, 36
Spatial Orientation
Published in Pamela S. Tsang, Michael A. Vidulich, Principles and Practice of Aviation Psychology, 2002
Coriolis forces refer specifically to the forces and linear accelerations that occur when a body attempts to move in a straight line within a reference frame that is in rotation with respect to a fixed (inertial) frame of reference. Early on this was referred to as the Coriolis phenomenon, even though no such explanation is required if one considers the semicircular canals as point sensors of angular acceleration. The name is retained in conjunction with the more applicable term cross-coupling.
Three-Dimensional Dynamic Modelling and Validation for Vibration of a Beam-Cable System
Published in Mathematical and Computer Modelling of Dynamical Systems, 2021
Mohammad Hadi Jalali, Geoff Rideout
where left superscript o indicates that the vector is defined in the inertial coordinate system, m is the mass and J is the rotational inertia. The first term in the right side of Equation (12) is the rotational inertia term and the second term is a gyrational term. Including forces such as gravity and equating vectors in different reference frames requires coordinate transforms from the body fixed frame to the inertial frame. This is accomplished with a rotation matrix. Rotation matrices are made for each of the three rotations about z, y and x axes, respectively. These matrices are multiplied together to create the transformation matrix. The final simplified rotation matrix is shown in the following equation that transforms coordinate frames from body fixed to inertial [21]: