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Here we show that a planetary system with initial quasi-circular, coplanar orbits would have evolved to the current orbital configuration, provided that Jupiter and Saturn crossed their 1 2 orbital resonance.
System dynamic equations of a discretized multi-degrees-of-freedom flexible system with initial joint clearances and joint actuators (active and viscoelastic passive) are derived.
When particles nucleate homogeneously in a polycrystalline system with initial grain radius ¯¯¯R0, many particles lie within the grains and the final grain size depends on ¯¯¯R0.
A coupled, rotating flexible wheelset, a flexible track model and a non-Hertzian/non-steady contact model have been implemented and results are presented here for a free wheelset on a symmetrical track system with initial random and sinusoidal roughness.
The stability and second-order response of multi-column system with initial geometric imperfections (i.e., made of columns with initial curvature, out-of-plumb in the plane of bending under eccentric axial loads at both ends), and non-linear end connections subjected to a lateral load at the top floor level are presented in a classical manner.
The state responses of the system with initial conditions (x t) = [0.1 0]^{T}) are given in Figure 2(a).
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Inducing thermal gradients in fluid systems with initial, well-defined density gradients results in the formation of distinct layered patterns, such as those observed in the ocean due to double-diffusive convection.
In this paper, an iterative learning control strategy is presented for a class of nonlinear pure-feedback systems with initial state error using fuzzy logic system.
To solve the identification problem for MIMO systems with initial values, this paper proposes a simple and efficient identification method containing the optimal input design.
Usual perturbative approaches usually cannot handle reliably (or at all) systems with initial states that are open shell and/or highly correlated (non-dynamical correlation) for either IPs or EAs.
Figure 4 shows the simulation result of synchronization of the chaotic systems with initial conditions: x 0 = (0.2, 0, 2) and x 0 ' = (0, 2.5,0).
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