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By introducing rotating Lagrangian coordinates, we eliminate the angular momentum rotation term from the CGPEs, which allows us to develop an efficient numerical method.
By applying a time-splitting technique for decoupling the nonlinearity and properly using the alternating direction implicit (ADI) technique for the coupling in the angular momentum rotation term in the GPE, at every time step, the GPE in rotational frame is decoupled into a nonlinear ordinary differential equation (ODE) and two partial differential equations with constant coefficients.
Note also the difference with (7) in the rotation term.
For orbits at radii (r_{B} simfrac{3}{2} r_{A}) however, the rotation term becomes dominant and the QBER shrinks to ∼10−10.
In this paper, we propose some efficient and robust numerical methods to compute the ground states and dynamics of Fractional Schrödinger Equation (FSE) with a rotation term and nonlocal nonlinear interactions.
Since there is no big frequency offset difference between stations after the coarse frequency offset synchronization, the inter-carrier-interference (ICI) term caused by the residual frequency offset is ignored for the simplicity in (1) whereas the accumulated phase rotation term caused by frequency offset is still included.
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Solving the present magneto elastic stress problem, dislocation and rotation terms appear, which makes the present problem complicate.
Rotation terms (nonlinear trigonometric functions) are integrated explicitly and correspond to a change in the reference configuration.
First, the objective function in the optimisation does not mix translation and rotation terms, which may have different scales.
A combination of increased hip adduction and internal rotation, decreased knee flexion, increased knee abduction and internal or external tibial rotation, termed "dynamic knee valgus", may increase the risk of ACL injury (Boden et al. 2009; Hewett et al. 2009; Hewett et al. 2006; Schmitz et al. 2008).
end{aligned} (34) The rotation terms being negligible, the result is essentially the same bound as in [8] for measurements of the Schwarzschild radius, namely (vert Delta r_{S}/r_{S} vert sim10^{-5}) for LEO orbits and (vert Delta r_{S}/r_{S} vert sim10^{-6}) for GEO orbits.
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