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Since the first is a second order equation of motion, the equations of motion must have two time derivatives.
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.
It is worthwile to cast the equation of motion in the dimensionless form.
The equation of continuity, equation of motion, penalty function and constitutive equation were simultaneously solved for velocity, using the Galerkin FEM.
Apart from the constitutive relations, the governing equations for displacement and temperature fields, as in the linear dynamical theory of classical thermoelasticity consist of the coupled partial differential equation of motion and the Fourier heat conduction equation.
Therefore, the equation of motion for upper homogeneous isotropic layer is
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.
For the elimination of this disadvantage, some authors suggest to multiply the damping part of the impact force by displacement; then the equation of motion during impact will be