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.
As a result of these acts, we are able to rewrite the equation of motion
for the nonlinear nonlocal model in the form
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
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.