Original scientific paper
Natural coordinates for an accelerated observer
Priyabrata Mitra
; Barasat Government College, Barasat, 24 Paraganas, West Bengal, India
S. Datta Majumdar
; Satyendranath Bose Institute of Physical Sciences, University College of Science, Calcutta - 700009, India
Abstract
The line element for an accelerated observer is derived by assuming linearity of transformation between his coordinates for any given time and a system of Galilean coordinates. It is noted that any 4 x 4 orthogonal matrix [a] with a14, a41 imaginary, a44 and other elements real represents a possible transformation from an inertial to an accelerated frame. Examples of such matrices are given and the associated angular velocities calculated. Finally, by a suitable interpretation of the Eulerian matrix giving the orientation of a rigid body in space the matrix representing the general motion of a frame on an inertial plane is obtained. The matrix contains a free parameter connected with the arbitrary rotational motion. This parameter becomes a definite function of time when the condition for irrotational motion is imposed and is represented by a time-integral directly related to the motion of the origin. The integral is evaluated in a closed form in special cases. The geodesic equations are then solved in a frame rotating with a constant angular velocity and moving with a constant acceleration along the axis of rotation and the motion of a free particle and a photon in such a frame is studied in arbitrary direction. Diagrams are drawn to illustrate the results.
Keywords
Hrčak ID:
328473
URI
Publication date:
3.1.1983.
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