The Earth is taken as a triaxial rigid body, which rotates freely in the Euclidian space. The starting equations are the Euler dynamic equations, with A smaller than B and B smaller than C. The Euler equations are sol...The Earth is taken as a triaxial rigid body, which rotates freely in the Euclidian space. The starting equations are the Euler dynamic equations, with A smaller than B and B smaller than C. The Euler equations are solved, and the numerical results are provided. In the calculations, the following parameters are used: (C-B)/A=0.003 273 53; (B-A)/C=0.000 021 96; (C-A)/B=0.003 295 49, and the mean angular velocity of the Earth's rotation, ω =0.000 072 921 15 rad/s. Calculations show that, besides the self-rotation of the Earth and the free Euler procession of its rotation, there exists the free nutation: the nutation angle, or the angle between the Earth's momentary rotation axis and the mean axis that periodically change with time. The free nutation is investigated.展开更多
Infinitesimal-rotation finite elements allow creating a linear problem that can be exploited to systematically reduce the number of coordinates and obtain efficient solutions for a wide range of applications,including...Infinitesimal-rotation finite elements allow creating a linear problem that can be exploited to systematically reduce the number of coordinates and obtain efficient solutions for a wide range of applications,including those governed by nonlinear equations.This paper discusses the limitations of conventional infinitesimal-rotation finite elements(FE)in capturing correctly the initial stress-free reference-configuration geometry,and explains the effect of these limitations on the definition of the inertia used in the motion description.An alternative to conventional infinitesimal-rotation finite elements is a new class of elements that allow developing inertia expressions written explicitly in terms of constant coefficients that define accurately the reference-configuration geometry.It is shown that using a geometrically inconsistent(GI)approach that introduces the infinitesimal-rotation coordinates from the outset to replace the interpolation-polynomial coefficients is the main source of the failure to capture correctly the reference-configuration geometry.On the other hand,by using a geometrically consistent(GC)approach that employs the position gradients of the absolute nodal coordinate formulation(ANCF)to define the infinitesimal-rotation coordinates,the reference-configuration geometry can be preserved.Two simple examples of straight and tapered beams are used to demonstrate the basic differences between the two fundamentally different approaches used to introduce the infinitesimal-rotation coordinates.The analysis presented in this study sheds light on the differences between the incremental co-rotational solution procedure,widely used in computational structural mechanics,and the non-incremental floating frame of reference formulation(FFR),widely used in multibody system(MBS)dynamics.展开更多
The analytic perturbation solutions to the motions of a planetary orbiter given in this paper are effective for 0e1, where e is the orbital eccentricity of the orbiter. In the solution, it is assumed that the rotation...The analytic perturbation solutions to the motions of a planetary orbiter given in this paper are effective for 0e1, where e is the orbital eccentricity of the orbiter. In the solution, it is assumed that the rotation of the central body is slow, and its astronomical background is clear. Examples for such planets in the solar system are Venus and Mercury. The perturbation solution is tested numerically on two Venusian orbiters with eccentric orbits, PVO and Magellan, and found to be effective.展开更多
Analogous to a black body, the empty space surrounding a massive body is theoretically envisioned to radiate thermal gravitational energy in accordance with Planck’s radiation law. Gravitational black-body radiation ...Analogous to a black body, the empty space surrounding a massive body is theoretically envisioned to radiate thermal gravitational energy in accordance with Planck’s radiation law. Gravitational black-body radiation offers a remarkably compelling solution to the deep, long-standing questions concerning galaxy rotation curves and strong gravitational lensing by large astrophysical systems, without the need to impose a dark matter or massive graviton hypothesis. As with the quantized orbits of the electron in the atom and the classical physics of Maxwell’s theory of electromagnetism, gravitational black-body radiation represents a truly profound break from the classical physics of Einstein’s general theory of relativity and the emergence of the fundamental quantum nature of gravity.展开更多
In this paper new matrices of the Cayley-Klein parameters are used to represent composition of several consecutive finite rotations of rigid body. The general commutative rules of multiplication for these matrices is ...In this paper new matrices of the Cayley-Klein parameters are used to represent composition of several consecutive finite rotations of rigid body. The general commutative rules of multiplication for these matrices is obtained. Furthermore, by using these matrices it is convenient to prove the theorem on finite rotation of rigid body. The result obtained in this paper is concise and easy to remember, and can be used to calculate vehicle attitude.展开更多
基金Funded by the National Natural Science Foundation of China (No.40574004).
文摘The Earth is taken as a triaxial rigid body, which rotates freely in the Euclidian space. The starting equations are the Euler dynamic equations, with A smaller than B and B smaller than C. The Euler equations are solved, and the numerical results are provided. In the calculations, the following parameters are used: (C-B)/A=0.003 273 53; (B-A)/C=0.000 021 96; (C-A)/B=0.003 295 49, and the mean angular velocity of the Earth's rotation, ω =0.000 072 921 15 rad/s. Calculations show that, besides the self-rotation of the Earth and the free Euler procession of its rotation, there exists the free nutation: the nutation angle, or the angle between the Earth's momentary rotation axis and the mean axis that periodically change with time. The free nutation is investigated.
基金supported,in part,by the National Science Foundation(Grant 1852510).
文摘Infinitesimal-rotation finite elements allow creating a linear problem that can be exploited to systematically reduce the number of coordinates and obtain efficient solutions for a wide range of applications,including those governed by nonlinear equations.This paper discusses the limitations of conventional infinitesimal-rotation finite elements(FE)in capturing correctly the initial stress-free reference-configuration geometry,and explains the effect of these limitations on the definition of the inertia used in the motion description.An alternative to conventional infinitesimal-rotation finite elements is a new class of elements that allow developing inertia expressions written explicitly in terms of constant coefficients that define accurately the reference-configuration geometry.It is shown that using a geometrically inconsistent(GI)approach that introduces the infinitesimal-rotation coordinates from the outset to replace the interpolation-polynomial coefficients is the main source of the failure to capture correctly the reference-configuration geometry.On the other hand,by using a geometrically consistent(GC)approach that employs the position gradients of the absolute nodal coordinate formulation(ANCF)to define the infinitesimal-rotation coordinates,the reference-configuration geometry can be preserved.Two simple examples of straight and tapered beams are used to demonstrate the basic differences between the two fundamentally different approaches used to introduce the infinitesimal-rotation coordinates.The analysis presented in this study sheds light on the differences between the incremental co-rotational solution procedure,widely used in computational structural mechanics,and the non-incremental floating frame of reference formulation(FFR),widely used in multibody system(MBS)dynamics.
文摘The analytic perturbation solutions to the motions of a planetary orbiter given in this paper are effective for 0e1, where e is the orbital eccentricity of the orbiter. In the solution, it is assumed that the rotation of the central body is slow, and its astronomical background is clear. Examples for such planets in the solar system are Venus and Mercury. The perturbation solution is tested numerically on two Venusian orbiters with eccentric orbits, PVO and Magellan, and found to be effective.
文摘Analogous to a black body, the empty space surrounding a massive body is theoretically envisioned to radiate thermal gravitational energy in accordance with Planck’s radiation law. Gravitational black-body radiation offers a remarkably compelling solution to the deep, long-standing questions concerning galaxy rotation curves and strong gravitational lensing by large astrophysical systems, without the need to impose a dark matter or massive graviton hypothesis. As with the quantized orbits of the electron in the atom and the classical physics of Maxwell’s theory of electromagnetism, gravitational black-body radiation represents a truly profound break from the classical physics of Einstein’s general theory of relativity and the emergence of the fundamental quantum nature of gravity.
文摘In this paper new matrices of the Cayley-Klein parameters are used to represent composition of several consecutive finite rotations of rigid body. The general commutative rules of multiplication for these matrices is obtained. Furthermore, by using these matrices it is convenient to prove the theorem on finite rotation of rigid body. The result obtained in this paper is concise and easy to remember, and can be used to calculate vehicle attitude.
