For first-order nonlinear nonholonomic systems,the present paper proves that the d-δ operations are commutative and derives the equation of motion without making use of the addition al Appell-Chetaev condition.This e...For first-order nonlinear nonholonomic systems,the present paper proves that the d-δ operations are commutative and derives the equation of motion without making use of the addition al Appell-Chetaev condition.This equation of motion coincides with the equation of'Vacco dynam- ics'.展开更多
This paper presents the integration methods for vacco dynmmies equations of nonlinear nonholononic system,First.vacco dynamies equations are written in the canonical form and the field form.second the gradient methods...This paper presents the integration methods for vacco dynmmies equations of nonlinear nonholononic system,First.vacco dynamies equations are written in the canonical form and the field form.second the gradient methods the single-componentmethods and the field method are used to integrate the dynamics equations of the corresponding holonomic system respectively.And considering the restriction of nonholonomic construint to the initial conditions the solutions of Vacco dynamics cquations of nonlinear nonholonomic system are obtained.展开更多
Using the method of [1], the present paper derives the Lagrange equation without multipliers for another class of first-order nonholonomic dynamical systems by means of variational principle. This kind of equations is...Using the method of [1], the present paper derives the Lagrange equation without multipliers for another class of first-order nonholonomic dynamical systems by means of variational principle. This kind of equations is also new.展开更多
Based on the theory of symmetries and conserved quantities, the exact invariants and adiabatic invariants of nonholonomic dynamical system of relative motion are studied. The perturbation to symmetries for the nonholo...Based on the theory of symmetries and conserved quantities, the exact invariants and adiabatic invariants of nonholonomic dynamical system of relative motion are studied. The perturbation to symmetries for the nonholonomic dynamical system of relative motion under small excitation is discussed. The concept of high-order adiabatic invariant is presented, and the form of exact invariants and adiabatic invariants as well as the conditions for their existence are given. Then the corresponding inverse problem is studied.展开更多
This paper uses Poincaré formalism to extend the Levi-Civita theorem to cope with nonholonomic sys- tems admitting certain invariant relations whose equations of motion involve constraint multipliers.Sufficient c...This paper uses Poincaré formalism to extend the Levi-Civita theorem to cope with nonholonomic sys- tems admitting certain invariant relations whose equations of motion involve constraint multipliers.Sufficient condi- tions allowing such extension are obtained and,as an application of the theory a generalization of Routh's motion is presented.展开更多
A mechanical model of skating motion was founded, and its solution was obtained by using the Routh's equations in nonholonomic dynamics. The two kinds of common, local meaning and scleronomic motions were discusse...A mechanical model of skating motion was founded, and its solution was obtained by using the Routh's equations in nonholonomic dynamics. The two kinds of common, local meaning and scleronomic motions were discussed in detail. The computational results turn out in good agreement with observations.展开更多
An incipient stage of a rotating drill string bit whirl motion proceeding on a well bottom surface is studied on the basis of kinematic （nonholonomic） models of mechanic interaction between the contacting uneven bod...An incipient stage of a rotating drill string bit whirl motion proceeding on a well bottom surface is studied on the basis of kinematic （nonholonomic） models of mechanic interaction between the contacting uneven bodies. The bit is considered to be an absolutely rigid spherical or ellipsoidal body, the well bottom surface can be plane or spherical. It is assumed that the system coaxiality is disturbed through small initial curvature of the drill string, imperfections of the bit and bore-well geometry or the system mass debalance. Linearized equations of the bit whirling are deducted, the frequencies of periodic motions are calculated, and their modes are constructed for different geometric parameters of the spherical and ellipsoidal bits. It is demonstrated that, depending on the system properties, the bit motion can acquire the regimes of forward and backward whMings or to transit to the state of stationary spinning relative to an immovable center of velocities. The most unfavorable and atypical whirling modes are characteristic for oblate eilipsoidal bits and curvilinear surfaces of the well bottom.展开更多
Nonlinear controllability and attitude stabilization are studied for the underactuated nonholonomic dynamics of a rigid spacecraft with one variable-speed control moment gyro （VSCMG）, which supplies only two interna...Nonlinear controllability and attitude stabilization are studied for the underactuated nonholonomic dynamics of a rigid spacecraft with one variable-speed control moment gyro （VSCMG）, which supplies only two internal torques. Nonlinear controllability theory is used to show that the dynamics are locally controllable from the equilibrium point and thus can be asymptotically stabilized to the equilibrium point via time-invariant piecewise continuous feedback laws or time-periodic continuous feedback laws. Specifically, when the total angular momentum of the spacecraft-VSCMG system is zero, any orientation can be a controllable equilib- rium attitude. In this case, the attitude stabilization problem is addressed by designing a kinematic stabilizing law, which is implemented through a nonlinear proportional and deriva- tive controller, using the generalized dynamic inverse （GDI） method. The steady-state instability inherent in the GDI con- troller is elegantly avoided by appropriately choosing control gains. In order to obtain the command gimbal rate and wheel acceleration from control torques, a simple steering logic is constructed to accommodate the requirements of attitude sta- bilization and singularity avoidance of the VSCMG. Illustrative numerical examples verify the efficacy of the proposed control strategy.展开更多
基金Project supported by the Science-Technology Foundation for Universities.
文摘For first-order nonlinear nonholonomic systems,the present paper proves that the d-δ operations are commutative and derives the equation of motion without making use of the addition al Appell-Chetaev condition.This equation of motion coincides with the equation of'Vacco dynam- ics'.
文摘This paper presents the integration methods for vacco dynmmies equations of nonlinear nonholononic system,First.vacco dynamies equations are written in the canonical form and the field form.second the gradient methods the single-componentmethods and the field method are used to integrate the dynamics equations of the corresponding holonomic system respectively.And considering the restriction of nonholonomic construint to the initial conditions the solutions of Vacco dynamics cquations of nonlinear nonholonomic system are obtained.
文摘Using the method of [1], the present paper derives the Lagrange equation without multipliers for another class of first-order nonholonomic dynamical systems by means of variational principle. This kind of equations is also new.
文摘Based on the theory of symmetries and conserved quantities, the exact invariants and adiabatic invariants of nonholonomic dynamical system of relative motion are studied. The perturbation to symmetries for the nonholonomic dynamical system of relative motion under small excitation is discussed. The concept of high-order adiabatic invariant is presented, and the form of exact invariants and adiabatic invariants as well as the conditions for their existence are given. Then the corresponding inverse problem is studied.
文摘This paper uses Poincaré formalism to extend the Levi-Civita theorem to cope with nonholonomic sys- tems admitting certain invariant relations whose equations of motion involve constraint multipliers.Sufficient condi- tions allowing such extension are obtained and,as an application of the theory a generalization of Routh's motion is presented.
文摘A mechanical model of skating motion was founded, and its solution was obtained by using the Routh's equations in nonholonomic dynamics. The two kinds of common, local meaning and scleronomic motions were discussed in detail. The computational results turn out in good agreement with observations.
文摘An incipient stage of a rotating drill string bit whirl motion proceeding on a well bottom surface is studied on the basis of kinematic （nonholonomic） models of mechanic interaction between the contacting uneven bodies. The bit is considered to be an absolutely rigid spherical or ellipsoidal body, the well bottom surface can be plane or spherical. It is assumed that the system coaxiality is disturbed through small initial curvature of the drill string, imperfections of the bit and bore-well geometry or the system mass debalance. Linearized equations of the bit whirling are deducted, the frequencies of periodic motions are calculated, and their modes are constructed for different geometric parameters of the spherical and ellipsoidal bits. It is demonstrated that, depending on the system properties, the bit motion can acquire the regimes of forward and backward whMings or to transit to the state of stationary spinning relative to an immovable center of velocities. The most unfavorable and atypical whirling modes are characteristic for oblate eilipsoidal bits and curvilinear surfaces of the well bottom.
基金supported by the Innovation Foundation of BUAA for Ph.D Graduatesthe Innovation Foundation of the National Laboratory of Space Intelligent Control
文摘Nonlinear controllability and attitude stabilization are studied for the underactuated nonholonomic dynamics of a rigid spacecraft with one variable-speed control moment gyro （VSCMG）, which supplies only two internal torques. Nonlinear controllability theory is used to show that the dynamics are locally controllable from the equilibrium point and thus can be asymptotically stabilized to the equilibrium point via time-invariant piecewise continuous feedback laws or time-periodic continuous feedback laws. Specifically, when the total angular momentum of the spacecraft-VSCMG system is zero, any orientation can be a controllable equilib- rium attitude. In this case, the attitude stabilization problem is addressed by designing a kinematic stabilizing law, which is implemented through a nonlinear proportional and deriva- tive controller, using the generalized dynamic inverse （GDI） method. The steady-state instability inherent in the GDI con- troller is elegantly avoided by appropriately choosing control gains. In order to obtain the command gimbal rate and wheel acceleration from control torques, a simple steering logic is constructed to accommodate the requirements of attitude sta- bilization and singularity avoidance of the VSCMG. Illustrative numerical examples verify the efficacy of the proposed control strategy.
