# equation of motion

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## equation of motion

[i′kwā·zhən əv ′mō·shən]
(fluid mechanics)
One of a set of hydrodynamical equations representing the application of Newton's second law of motion to a fluid system; the total acceleration on an individual fluid particle is equated to the sum of the forces acting on the particle within the fluid.
(mechanics)
Equation which specifies the coordinates of particles as functions of time.
A differential equation, or one of several such equations, from which the coordinates of particles as functions of time can be obtained if the initial positions and velocities of the particles are known.
(quantum mechanics)
A differential equation which enables one to predict the statistical distribution of the results of any measurement upon a system at any time if the initial dynamical state of the system is known.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
Applying the equation of motion of the mass density, i.e., (57), on (59), the equation of motion of the current density, i.e., (58), can be further simplified as follows:
In this case, the analog of (28) can be derived and all the used majorant bounds can be applied for the proof of the existence of periodic solution of the considered equation of motion.
The fractional Hamiltonian equation of motion can be determined as follow
In this case, the runaway and causal problems are eliminated and the exact equation of motion of a charged particle was recently given by Rohlrich  and Yaghjian .
Substituting (2) into (1) and differentiating both sides of the resulting equation with respect to x, we rewrite the equation of motion for the strain [U.sub.X].
In the latter case, having found the possible solutions of the equation of motion, one has to face the issue of the appropriate weighed average of the associated energy losses.
It may be obtained if the structure velocity term in the Morison equation is transferred from the force vector on right hand side to the damping term on the left hand side in the governing equation of motion. The structural damping follows Eq.
We now use our nonlinear transformation approach to find the equivalent equation of motion of the damped pendulum equation 
The above equation of motion of particles can also derive from Equation (5) by another method.
The introductory chapter addresses dynamic response, formulation of the equation of motion, dynamic degrees of freedom, modeling, analysis, and testing.
We now consider the equation of motion of yarn (Pracek, 2002):

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