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The motion equations are derived applying the Hamilton principle.
Firstly, the relative motion equations are derived in the body-Line of Sight (LOS) coordinate system.
Motion equations are obtained by means of Hamilton's principle and solved analytically.
Considering size effects based on Eringen's nonlocal theory, motion equations are derived using Hamilton's principle and solved by Galerkin's method.
Standard submarine motion equations are the most used hydrodynamic model, in which more than 100 coefficients need to be estimated.
For high speed maneuvers, rigid motion equations are used to correct the measurements of the gravitational acceleration.
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The insertion of supports – a two-degree-of-freedom isolation system - into rotor's motion equations is performed in two different ways: (1) by adding degrees of freedom and (2) by using the GEP technique.
For particle phase, the Monotonic Upstream Schemes for Conservation Laws as well as the solution of the Riemann problem for the particle motion equations is also used together with the schemes above.
The differential operators corresponding to the Legendre differential equation and the harmonic motion equation are self-adjoint, while those corresponding to the Laguerre differential equation and Hermite differential equation are not.
The motion equation is derived based on the classical plate theory and solved by using Galerkin method.
In this work, the vehicle motion equation is reformulated in terms of the kinetic energy of the moving vehicle which leads to a linear differential equation without loss of information.
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