equation of motion


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e·qua·tion of mo·tion

(ĕ-kwā'zhŭn mō'shŭn)
1. An expression of Newton's second law that relates forces, displacements, and their derivatives for a mechanical system.
2. For the respiratory system, an equation that relates the forces involved in breathing to the displacements they produce. Typically, pressure differences are used to represent generalized forces and volume changes are used to represent generalized displacements. The simplest equation of motion written for the lungs states that the change in transpulmonary pressure is equal to the sum of an elastic term plus a flow resistive term: transpulmonary pressure change = elastance × tidal volume + resistance × change in flow.

equation of motion

A statement of the variables of pressure, volume, compliance, resistance, and flow for respiratory system mechanics.
See also: equation
References in periodicals archive ?
Skrypnik, "Periodic and bounded solutions of the Coulomb equation of motion of two and three point charges with equilibrium in the line," Ukrainian Mathematical Journal, vol.
which is the same with Euler-Lagrangian equation of motion.
For the field acting on the centre of mass, the particle mass and charge appear as if they are at the centre of mass point and we treat the equation of motion of the particle in the point particle limit.
This rigid body momentum can be transformed into the global coordinate system and differentiated with respect to time to obtain the body equation of motion as follows:
To find the equation of motion for the magnetization subjected to a magnetic field oscillating along the z-axis, the following vectors have to be inserted into (13): H(t) = (0,0, [H.sub.0] cos([omega]t)), M x H = ([[omega].sub.L]/[[mu].sub.0][absolute value of ([absolute value of (y)))([M.sub.y] cos([omega]t), -[M.sub.x] cos ([omega]t), 0), and [M.sub.eq](H) = (0,0, [phi][M.sub.d]L(([[mu].sub.0][M.sub.d]V[H.sub.0]/kT) cos([omega]t))), where [[omega].sub.L] = [[mu].sub.0] [absolute value of (y)][H.sub.0].
Therefore, the equation of motion for the spar hull leads to
In this case, we assume that, besides the nonlinear irrational restoring force due to the stretched wires, we have a damper attached to the mass system, and hence, the nonlinear differential equation of motion for a single-degree-of-freedom system can be written as
Therefore, we can confirm that the microscopic particles in the nonlinear quantum mechanics satisfy the Newton type equation of motion for a classical particle.
It is worthwile to cast the equation of motion in the dimensionless form.
His topics include LaGrangian and Hamiltonian formalism, and the relation between relativity and essential tensor calculus, along with Einstein's equation in special cases with explicit presentations of calculations for all steps, with coverage of Newtonian mechanics, symmetries, bodies' central forces, rigid body dynamics, small oscillations and stability, phenomenological consequences, aspects of special relativity, the equation of motion of the particle in a gravitational field, tensor calculus for Reimann spaces, Einstein's equation of the gravitational field, and the Schwarzschild solution.