ELLIPTIC MOTIONS ON MODAL CONVERSION ULTRASONIC MOTORS

The forming of elliptic motions on the modal conversion ultrasonic motors （MCUMs） is discussed. The principles of the modal conversion are investigated based on the coupling with the stator and the rotor, and using an independent coupler. The elliptical locus observed on the longitudinal-torslonal vibration converter with oblique slits is analyzed by using vibration theory. A method for the modal conversion is proposed by using the local mode of a substructure On a main structure. The method can be used to design the modal conversion type ultrasonic motors.

Canonical Treatment of Elliptical Motion

The constrained motion of a particle on an elliptical path is studied using Hamiltonian mechanics through Poisson bracket and Lagrangian mechanics through Euler Lagrange equation using non-natural Lagrangian. We calculate the generalized momentum pθ and we find that this quantity is not conserved and the conjugate θ coordinate is not a cyclic coordinate.

Design and control of multiple spacecraft formation flying in elliptical orbits

Spacecraft formation flying is an attractive new concept in international aeronautic fields because of its powerful functions and low cost. In this paper, the formation design and PD closed-loop control of spacecraft formation flying in elliptical orbits are discussed. Based on two-body relative dynamics, the true anomaly is applied as independent variable instead of the variable of time. Since the apogee is considered as the starting point, the six integrating constants are calculated. Therefore, the algebraic solution is obtained for the relative motion in elliptical orbits. Moreover, the formation design is presented and both circular formation and line formation are provided in terms of an algebraic solution. This paper also discusses the PD-closed loop control for precise formation control in elliptical orbits. In this part, the error-type state equation is put forward and the linear quadratic regulator （LQR） method is used to calculate PD parameters. Though the gain matrix calculated from LQR is time-variable because the error-type state equation is time variable, the PD parameters are also considered as constants because of their small changes in simulation. Finally, taking circular formation as an example, the initial orbital elements are achieved for three secondary spacecraft. And the numerical simulation is analyzed under PD formation control with initial errors and J2 perturbation. The simulation results demonstrate the validity of PD closed-loop control scheme.

NEW TYPE OF LINEAR ULTRASONIC MOTOR WITH TWO DEGREES OF FREEDOM USING LONGITUDINAL AND BENDING MODE

A new type of linear ultrasonic motor with two degrees of freedom (DOF) motion is presented. The concept of the new typical motor is based on the combination of a longitudinal and two bending modes. The construction and the operational principle of motor are described, and the elliptical motion of the driving point of the actuator is proved. Meanwhile, a prototype linear motor is designed by using the finite element method (FEM) and is constructed for experiments. The vibration modes are tested with the laser doppler vibrometer (PSV-300F), and the experimental results prove that the design requirements on the mode shape of the actuator and nature frequency are satisfied. The test run of the motor indicates that the operational principle of the motor and the design results are correct, and the output properties are also tested.

Optimal design of V-type ultrasonic motor

V-type ultrasonic linear motor fabricated using a simple punching technique was proposed to utilize as an actuator of small precision machine.The stator of the motor is composed of a thin elastic body and four ceramics attached to the upper and bottom areas of the body.The ceramics have each direction of polarization.When two harmonic voltages with a 90° phase difference are applied to the ceramics,symmetric and anti-symmetric displacements will generate at the tip to produce an elliptical motion.A finite element analysis(ATILA) was conducted to simulate the motion pattern for the contact tip of the stator.To develop a model that generates the maximum displacement at contact tip,the FEM program was used for various lengths.In addition,an optimal model was chosen by considering the magnitude and shape of the displacement according to changes in frequency.The maximum elliptical displacement is shown by W2L11 model,which has a ratio of ceramic width to length of 1:5.5.However,the displacement of the contact tip is reduced by the bucking phenomenon if the ratio is larger than 1:6.

Ellipticity of motion of particle in field of inhomogeneous plane wave

The elliptic motion of particle in the fields of the inhomogeneous plane wavs that are generated on a liquid thermoviscoelastic solid interface is studied.. Calculations show that the ellipticity of the motion of Particle is related to the incident angle that the homogeneous plane wave incidents upon the interface. The influeree of viscous properties of solid on the ellipticity of particle's motion is small and shows near the critical angles of longitudinal and transversal wavs. Under the incidence at Rayleigh angle, the change of the ellipticity of motion of the particle is periodic in the wake of its Rayleigh wavelength and its elliptic locus is couoter clockwise and clockwise rotation periodically.

New Solution for the Earth’s Free Wobble and Its Geophysical Implications

In this paper, the theory of the free wobble of the triaxial Earth is developed and new conclusions are drawn: the Euler period should be actually expressed by the first kind of complete elliptic integral; the trace of the free polar motion is elliptic and the orientations of its semi-minor and major axes are approximately parallel to the Earth's principal axes A and B, respectively. In addition, the present theory shows that there is a mechanism of frequency-amplitude modulation in the Chandler wobble, which might be a candidate for explaining the correlation between the amplitude and period of the Chandler wobble.