An invariant formulation of the potential integration method for the vortical equation of motion of a material point

A V Kukushkin

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An invariant formulation of the potential integration method for the vortical equation of motion of a material point

机译：物质点运动涡旋方程势积分方法的不变式

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A relativistic procedure for deriving the kinetic part of the generalized Euler equation is proposed as an argument to justify the application of the vortical equation of motion to the solution of classical discrete dynamics problems. An invariant formulation of the potential integration method for th vortical equation of motion is given for a definite class of two-dimensional motions. To demonstrate the efficiency of the method, a number of well-known theorems on the dynamics of a material point are proved. A new result of the study is the fact that zeroenergy hyperelliptic motions are related to the field of 'multi-plicative' type forces.

机译：提出了一种相对论性的方法来推导广义欧拉方程的动力学部分，以此作为论证将涡旋运动方程应用到经典离散动力学问题的求解中的理由。对于一类确定的二维运动，给出了运动热方程的势积分方法的不变式。为了证明该方法的有效性，证明了许多关于材料点动力学的众所周知的定理。该研究的新结果是零能量超椭圆运动与“倍增”型力领域有关。

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《Physics - Uspekhi》 |2002年第11期|共12页
作者
A V Kukushkin;
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正文语种 eng
中图分类物理学;
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1. An invariant formulation of the potential integration method for the vortical equation of motion of a material point [J] . A V Kukushkin Physics - Uspekhi . 2002,第11期

机译：物质点运动涡旋方程势积分方法的不变式
2. Orthogonal spline collocation methods for the stream function-vorticity formulation of the Navier-Stokes equations [J] . Fairweather G, Ma HP, Sun WW Numerical Methods for Partial Differential Equations: An International Journal . 2008,第2期

机译：Navier-Stokes方程的流函数-涡度公式化的正交样条搭配方法
3. Methods of Solution of the Velocity-Vorticity Formulation of the Navier-Stokes Equations [J] . S. C. R. DENNIS, J. D. HUDSON Journal of Computational Physics . 1995,第2期

机译：Navier-Stokes方程的速度-涡度公式的求解方法
4. Scale Invariant forms of Cauchy, Euler, Navier-Stokes and Modified Equation of Motion and Helmholtz Vorticity Equation [C] . SIAVASH H. SOHRAB Advances in fluid mechanics amp; heat amp; mass transfer . 2012

机译：Cauchy，Euler，Navier-Stokes的尺度不变形式以及运动的修正方程和亥姆霍兹涡度方程
5. Development and evaluation of matrix material formulations for potential integration into immunodiagnostic biosensors. [D] . Aminayi, Payam. 2016

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6. A Crank–Nicolson finite spectral element method for the 2D non-stationary Stokes equations about vorticity–stream functions [O] . Yanjie Zhou, Zhendong Luo, Fei Teng -1

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7. A scale-invariant formulation of the anticipated potential vorticity method [O] . Chen, Qingshan, Gunzburger, Max, Ringler, Todd 2011

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8. Multigrid Method for an Invariant Formulation of the Incompressible Navier-StokesEquations in General Coordinates [R] . Oosterlee, C. W. 1991

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An invariant formulation of the potential integration method for the vortical equation of motion of a material point

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