Search

An alternative proof for the explicit equations of motion for mechanical systems with independent non-ideal constraints is proposed in this paper. These equations are derived without the use of generalized inverse matrices and based on the decomposition of the constraint forces along the acceleration-constrained flat surface and its normal plane.

In this paper, we proposed a method of deriving equations of motion, which is free of Lagrange multipliers, for a constrained dynamical system with emphasis on its suitability for nonlinear nonholonomic constraints. A local coordinate space is established on the basis of a scaled acceleration-constrained flat surface and the corresponding normal space. Constraint forces are decomposed into components along this local coordinate space. The normal components of constraint forces are determined by the motion of the system and constraints, and the tangential components are arbitrary. Then Gauss' principle of least constraint is employed to minimize the tangential components so as to derive the equations of motion in explicit form. An example demonstrating the general equations derived here is provided.

The Miller-indices determination of the arising surfaces at the Si(0 0 1) convex corner due to anisotropic etching is investigated. We propose a 2D zoning model in which the undercut planes arising at a masked convex corner are presumed to be in the same zone as the sidewalls forming the convex corner, which is characterized by the parallelism of the intersection lines of each pair of new surfaces and the sidewalls. Based on this model a method combining the experimental data, analytical geometry and stereographic projection is presented to systematically determine the Miller indices of the arising planes. The quantitative prediction of undercut planes is confirmed by the angle measurement using a surface profiler.