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
Under the traditional dynamic model,the conventional method for solving the rotation angle of a rigid body is to use the fixed-axis rotation law of the rigid body,but the known rotation shaft position must be used as ...Under the traditional dynamic model,the conventional method for solving the rotation angle of a rigid body is to use the fixed-axis rotation law of the rigid body,but the known rotation shaft position must be used as a prerequisite.In practical work,for the rotation of a rigid body under multiple forces,solving the shaft is often a difficult problem.In this paper,we consider the rigid body of the disc is subjected to the force of uneven magnitude from multiple angles,the position of the rotating shaft is obtained by iterative inversion through the rigid body rotation law and the dichotomy method.After the position of the shaft is determined,we establish a differential equation model based on the law of rigid body rotation,the rotation angle of the rigid body thus being solved based on this model.Furthermore,an optimization algorithm such as genetic algorithm is used to search for a correction scheme to return the rigid body to equilibrium at any given deflection angle.The model and method are based on computer to explore the law of rotation,the practical application of them play an important role in studying the concentric drum movement and the balance of handling furniture.展开更多
Based on the basic theory of electrodynamics about electromagnetic radiation,the general formulae of radiation power and damping torque of electric-quadrupole moment for a steadily and uniformly charged rigid body wit...Based on the basic theory of electrodynamics about electromagnetic radiation,the general formulae of radiation power and damping torque of electric-quadrupole moment for a steadily and uniformly charged rigid body with any periodic rotation are derived.The concise form of the formulae in some special symmetric cases are deduced and discussed,and the results of several common symmetric charged bodies are listed.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.
文摘Under the traditional dynamic model,the conventional method for solving the rotation angle of a rigid body is to use the fixed-axis rotation law of the rigid body,but the known rotation shaft position must be used as a prerequisite.In practical work,for the rotation of a rigid body under multiple forces,solving the shaft is often a difficult problem.In this paper,we consider the rigid body of the disc is subjected to the force of uneven magnitude from multiple angles,the position of the rotating shaft is obtained by iterative inversion through the rigid body rotation law and the dichotomy method.After the position of the shaft is determined,we establish a differential equation model based on the law of rigid body rotation,the rotation angle of the rigid body thus being solved based on this model.Furthermore,an optimization algorithm such as genetic algorithm is used to search for a correction scheme to return the rigid body to equilibrium at any given deflection angle.The model and method are based on computer to explore the law of rotation,the practical application of them play an important role in studying the concentric drum movement and the balance of handling furniture.
基金Supported by the National Natural Science Foundation of China(12074295)
文摘Based on the basic theory of electrodynamics about electromagnetic radiation,the general formulae of radiation power and damping torque of electric-quadrupole moment for a steadily and uniformly charged rigid body with any periodic rotation are derived.The concise form of the formulae in some special symmetric cases are deduced and discussed,and the results of several common symmetric charged bodies are listed.
