Symplectic analysis on orbit-attitude coupling dynamic problem of spatial rigid rod

An orbit-attitude coupling dynamic model for the spatial rigid rod that is abstracted from the large-stiffness slender components widely used in spatial structures is established, and the symplectic method is used to estimate the validity of the dynamic model by analyzing the coupling dynamic behaviors of the rod in this work. Based on the Hamiltonian variational principle, the orbit-attitude dynamic model of the spatial rigid rod is proposed, and the canonical form of the model is presented first. Then, the symplectic Runge–Kutta method is developed, and the structure-preserving properties of the canonical form, including the conservation law of energy and conservative property in the phase space, are investigated to illustrate the validity of the numerical results obtained by the symplectic Runge–Kutta method subsequently. Finally, the effects of the nonspherical perturbations of the Earth on the coupling dynamic behaviors are investigated numerically. From the simulation results, it can be concluded that the main orbit-attitude coupling dynamic behaviors of the spatial large-stiffness slender component excited by the nonspherical perturbation can be described by the proposed dynamic model ignoring the deformation as well as the transverse vibration of the slender component, which provides an approach for simplifying rapid dynamic analysis on the spatial large-stiffness slender component. In addition, the validity and the structure-preserving properties of the symplectic Runge–Kutta method for the orbit-attitude coupling dynamic problem of the spatial rigid rod are also illustrated.

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Application of the piecewise constant method in nonlinear dynamics of drill string

International Journal of Nonlinear Sciences and Numerical Simulation ◽

10.1515/ijnsns-2019-0167 ◽

2021 ◽

Vol 0 (0) ◽

Author(s):

Jialin Tian ◽

Jie Wang ◽

Yi Zhou ◽

Lin Yang ◽

Changyue Fan ◽

...

Keyword(s):

Nonlinear Dynamics ◽

Dynamic Model ◽

Dynamic Characteristics ◽

Drill String ◽

Vibration Velocity ◽

Kutta Method ◽

Time Step ◽

Piecewise Constant ◽

Runge Kutta Method ◽

Runge Kutta

Abstract Aiming at the current development of drilling technology and the deepening of oil and gas exploration, we focus on better studying the nonlinear dynamic characteristics of the drill string under complex working conditions and knowing the real movement of the drill string during drilling. This paper firstly combines the actual situation of the well to establish the dynamic model of the horizontal drill string, and analyzes the dynamic characteristics, giving the expression of the force of each part of the model. Secondly, it introduces the piecewise constant method (simply known as PT method), and gives the solution equation. Then according to the basic parameters, the axial vibration displacement and vibration velocity at the test points are solved by the PT method and the Runge–Kutta method, respectively, and the phase diagram, the Poincare map, and the spectrogram are obtained. The results obtained by the two methods are compared and analyzed. Finally, the relevant experimental tests are carried out. It shows that the results of the dynamic model of the horizontal drill string are basically consistent with the results obtained by the actual test, which verifies the validity of the dynamic model and the correctness of the calculated results. When solving the drill string nonlinear dynamics, the results of the PT method is closer to the theoretical solution than that of the Runge–Kutta method with the same order and time step. And the PT method is better than the Runge–Kutta method with the same order in smoothness and continuity in solving the drill string nonlinear dynamics.

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Dynamic Response of SFD-Sliding Rigid Bearing Rotor -System

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.706-708.1310 ◽

2013 ◽

Vol 706-708 ◽

pp. 1310-1313

Author(s):

Ji Yan Wang

Keyword(s):

Dynamic Response ◽

Dynamic Model ◽

Periodic Motion ◽

Rotor System ◽

Rigid Rotor ◽

Kutta Method ◽

Sliding Bearing ◽

Runge Kutta Method ◽

Stable Periodic ◽

Runge Kutta

This paper establishes a linking dynamic model of SFD-sliding bearing rigid rotor system by employing Runge-Kutta method to solve dynamic question of the above systems. The study has shown: rigid rotor system can keep stable periodic motion in a certain scope with the following quasi-periodicity bifurcation.

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Structure-Preserving Analysis of Skeleton Structure of Solar Sail in the Deploying Process

Xibei Gongye Daxue Xuebao/Journal of Northwestern Polytechnical University ◽

10.1051/jnwpu/20183620302 ◽

2018 ◽

Vol 36 (2) ◽

pp. 302-307

Author(s):

Tingting Yin ◽

Zichen Deng ◽

Weipeng Hu ◽

Xindong Wang

Keyword(s):

Dynamic Model ◽

Phased Array ◽

Lagrange Equation ◽

Solar Sail ◽

Symplectic Method ◽

Kutta Method ◽

Runge Kutta Method ◽

System Energy ◽

Runge Kutta ◽

Skeleton Structure

For the simplified dynamic model of the skeleton structure of solar sail in the solar power satellite via arbitrarily large phased array system (SPS-ALPHA) in the deploying process, the symplectic method is employed to simulate the dynamic behaviors of the skeleton structure of solar sail and the characteristic of vibration, the constraints default as well as the energy-preserving of the system are all discussed in this paper.Firstly, the simplified dynamic model of the skeleton structure is established based on the variational principle, which is rewritten in the form of the associated canonical equation in Hamilton framework from the Lagrange equation that describes the deploying process of the skeleton structure of solar sail. And then, the equation is numerically simulated by the symplectic Runge-Kutta method and the classical Runge-Kutta method respectively. Comparing with the classical Runge-Kutta method, the symplectic Runge-Kutta method employed in this paper can preserve the displacement constraint and the system energy well with excellent numerical stability.

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