The Motion and Control of a Chaplygin Sleigh with Internal Shape in an Ideal Fluid

[摘要] In this dissertation we will examine a nonholonomic system with Lie group symmetry: theChaplygin sleigh coupled to an oscillator moving through a potential fluid in two dimensions.This example is chosen to illustrate several general features. The sleigh system in the planehas SE(2) symmetry. This group symmetry will be used to separate the dynamics of thesystem into those along the group directions and those not. The oscillator motion is not alongthe group and so acts as an additional configuration space coordinate that plays the roleof internal ;;shape.;; The potential fluid serves as an interactive environment for the sleigh.The interaction between the fluid and sleigh depends not only on the sleigh body shapeand size but also on its motion. The motion of the sleigh causes motion in the surroundingfluid and vice-versa. Since the sleigh body is coupled to the oscillator, the oscillator willhave indirect interaction with the fluid. This oscillator serves as internal shape and interactswith the external environment of the sleigh through its coupling to the sleigh body and thenonholonomic constraint; it will be shown that this interaction can produce a variety of typesof motion depending on the sleigh geometry. In particular, when the internal shape of thesystem is actively controlled, it will be proven that the sleigh can be steered through the planetowards any desired position. In this way the sleigh-fluid-oscillator system will demonstratehow a rigid body can be steered through an interactive environment by controlling things wholly within the body itself and without use of external thrust.

[发布机构] University of Michigan

[效力级别] Chaplygin Sleigh

[关键词] Nonholonomic Mechanics;Chaplygin Sleigh;Physics;Science;Physics