國立臺灣大學應用力學研究所鮑亦興2006-07-262018-06-292006-07-262018-06-292005-07-31http://ntur.lib.ntu.edu.tw//handle/246246/21738In dealing with the mechanics of material bodies modeled by particles, rigid body, or deformable body subject to various types of constraint, variational principles can usually provide a suitable path to obtain the solutions. The main objective of this project is to seek additional applications and possible extensions on the basis of the Principle of Virtual Power, and to explore whether the proposed principle can be unified with the law of thermodynamics to form a unified variational principle. After nearly two-year term of endeavor, we are able to obtain the desired Principle by choosing the velocity and the velocity gradient as fundamental variables in mechanics, and the entropy and the hear flux as the fundamental quantities in theomodynamics. The Principle indeed unify the theory of thermodynamics and continuum mechanics, from which a variational equation can be established. The Cauchy’s laws of linear and angular momentum and the newly developed variational constitutive law are then deduced. By selecting appropriate internal energy function and dissipating function, we have derived the constitutive equations for elastic body or viscous fluid in mechanics, and Fourier law and Maxwell-Catteneo Equation in the first year. In the second year, we established the constitutive laws for the thermo-viscous fluid and micro-polar material. See Part I of this report for more details. On the other hand, in the aspect of tracking control, we have used the Reduced Appell Equation to construct equations of motion of the privileged coordinates, and found that the equations are decoupled from the non-privileged coordinates in the first year. The fuzzy controller and sliding mode controller were then used to design the tracking control loop. This year, we adopt the backstepping method applied to the chained form of the kinematic equation to compute the compensated values for the privileged variables. Simulation results on the tracking control of wheeled vehicle show that the performance is excellent. The results are shown in Part II of this report.application/pdf832228 bytesapplication/pdfzh-TW國立臺灣大學應用力學研究所Continuum MechanicsThermodynamicsPrinciple of Virtual PowerPrivileged CoordinatesTracking Controlreporthttp://ntur.lib.ntu.edu.tw/bitstream/246246/21738/1/932212E002026.pdf