To obtain the equation of motion
of the machine, the expression (1) should be considered in conjunction with equation (2).
The main goal of this work is to derive the equation of motion
in fractional form for the single fluid from the fractional Lagrangian density and from the fractional Hamiltonian density also to determine the energy-stress tensor in fractional form also, by using Caputo's fractional derivative.
Solves equation of motion
(16) for clutch engagement
In Rueda's approach, the classical particle was considered as a homogeneously charged rigid sphere and to find the energy absorbed by the particle, the radiation damping and binding terms were neglected when compared to the force term in the Lorentz Abraham equation of motion
The differential equation of motion
for three dimensions vibration of a frame pipe carrying a moving fluid is :
In the absence of body forces the equation of motion
for a one-dimensional, homogeneous, elastic medium is
The integration of the differential equation of motion
is calculated assuming that the acceleration is constant for small steps (Euler's integration).
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 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):
The pressure component was excluded from the equation of motion
by relating pressure to the equation of continuity manipulated by the huge constant penalty number [[lambda].