Second-Order Analytical Solution of Relative Motion in J2-Perturbed Elliptic Orbits

2018 ◽  
Vol 41 (10) ◽  
pp. 2258-2270 ◽  
Author(s):  
Zhen Yang ◽  
Ya-Zhong Luo ◽  
Jin Zhang
Keyword(s):  
Analytical Solution ◽  
Relative Motion ◽  
Second Order ◽  
Elliptic Orbits

Second-order state transition for relative motion near perturbed, elliptic orbits

2006 ◽  
Vol 97 (2) ◽  
pp. 101-129 ◽  
Author(s):  
Prasenjit Sengupta ◽  
Srinivas R. Vadali ◽  
Kyle T. Alfriend
Keyword(s):  
Relative Motion ◽  
State Transition ◽  
Second Order ◽  
Elliptic Orbits ◽  
Order State

Relative Motion of Particles in Coplanar Elliptic Orbits

1979 ◽  
Vol 2 (5) ◽  
pp. 443-446 ◽  
Author(s):  
Terry Berreen ◽  
George Svedt
Keyword(s):  
Relative Motion ◽  
Elliptic Orbits

Study on the Method of the Damage Identification for Frame Structure

2012 ◽  
Vol 204-208 ◽  
pp. 2824-2831
Author(s):  
You Fa Yang ◽  
Shuai Li ◽  
Ling Ling
Keyword(s):  
Analytical Solution ◽  
Iterative Algorithm ◽  
Taylor Series ◽  
Structural Damage ◽  
Damage Identification ◽  
Second Order ◽  
Bias Error ◽  
Dynamic Data ◽  
First Order ◽  
Sensitivity Equations

First order iterative algorithm, mixed iterative algorithm, structural damage identification using static and dynamic data were put forward. The first and second order sensitivity matrixes of modal parameters that respect to the damage member were derived, and the modal truncation error which produced during the derivation of modal mode sensitivity was improved. The first and second order sensitivity equations were established respectively based on the principle of Taylor series expansion. And the solving method of these sensitivity equations was studied. Mixed iterative algorithm took up the second order nonlinear analytical solution as the first substituting value, and then the first substituting value was modified based on the Taylor series bias error using the solution of the first order sensitivity equation. It showed that the mixed iterative algorithm in this paper had a better convergence and a faster iteration speed because the higher precision second order nonlinear analytical solution was adopted. Because the method using static and dynamic data combined the static information and dynamic information of the structure, it could react the inside information of the structure more comprehensively, the result of damage identification was more accurate and it would be adapted more widely.

Analysis of Motion of the Impact-Dry-Friction Pair of Bodies and its Application to the Investigation of the Impact Dampers Dynamics

1999 ◽  
Author(s):  
František Peterka
Keyword(s):  
Analytical Solution ◽  
Numerical Simulations ◽  
Mechanical System ◽  
Relative Motion ◽  
Dry Friction ◽  
Friction Pair ◽  
Strong Nonlinearity ◽  
Friction Forces ◽  
The Impact ◽  
Analysis Of Motion

Abstract The motion with impacts and dry friction forces appears in some mechanical systems as mechanisms with clearances, (e.g., in gearings, pins, slots, guides, valve gears etc.), impact dampers, relays, forming and mailing machines, power pics etc. Such mechanisms include one or more pairs of impacting bodies, which introduce the strong nonlinearity into the system motion. The motion of the general pair of bodies with the both-sides impacts and dry friction forces is assumed (Fig.1). It can be the part of a more complex chain of masses in the mechanical system. Dead zones in the relative motion of bodies can be caused by assumed nonlinearities. The mathematical conditions controlling the numerical simulations or analytical solution of the motion are introduced. The application of this method is explained by the study of the influence of dry friction force on amplitude-frequency characteristics of four types of dynamical and impact dampers with optimised parameters.

Added Stability Lobes in Machining Processes That Exhibit Periodic Time Variation, Part 1: An Analytical Solution

2004 ◽  
Vol 126 (3) ◽  
pp. 467-474 ◽  
Author(s):  
William T. Corpus ◽  
William J. Endres
Keyword(s):  
Numerical Simulation ◽  
Analytical Solution ◽  
Closed Form ◽  
High Speed ◽  
Stability Limit ◽  
Second Order ◽  
Machining Processes ◽  
Stability Lobes ◽  
Time Varying Systems ◽  
Computationally Intensive

An added family of stability lobes, which exists in addition to the traditional stability lobes, has been identified for the case of periodically time varying systems. An analytical solution of arbitrary order is presented that identifies and locates multiple added lobes. The stability limit solution is first derived for zero damping where a final closed-form symbolic result can be realized up to second order. The un-damped solution provides a mathematical description of the added lobes’ locations along the speed axis, an added-lobe numbering convention, and the asymptotes for the damped case. The derivation for the damped case permits a final closed-form symbolic result for first-order only; the second-order solution requires numerical evaluation. The easily computed analytical solution is shown to agree well with the results of the computationally intensive numerical simulation approach. An increase in solution order improves the agreement with numerical simulation; but, more importantly, it allows equivalently more added lobes to be predicted, including the second added lobe that cuts into the speed regime of the traditional high-speed stability peak.

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