Finding out normal coordinates with the method of undetermined coefficients: An alternative starting point of solving a small oscillation problem with two degrees of freedom

doi:10.1177/0306419016637488

CORC > 北京大学 > 信息科学技术学院

	Finding out normal coordinates with the method of undetermined coefficients: An alternative starting point of solving a small oscillation problem with two degrees of freedom
	Zhang, Gengmin
刊名	International Journal of Mechanical Engineering Education
	2016
DOI	10.1177/0306419016637488
英文摘要	A small oscillation with s degrees of freedom can be decomposed into s independent oscillations with one degree of freedom with the aid of normal coordinates. In the mainstream solution strategy, the normal coordinates are usually found out after the motion of the system has already been worked out using Lagrange's equations. In this article, the search for the normal coordinates is used as the starting point of solving the problems with s = 2. For this purpose, the coefficients in the linear transformation from a set of generalized coordinates to a set of normal coordinates are treated as undetermined coefficients. The equations these undetermined coefficients must satisfy are deduced and solved. In comparison with the mainstream method, the dependence of the generalized coordinates on the time can be worked out in a more straightforward manner using the method of undetermined coefficients in the s = 2 case. Especially, even when the two angular frequencies degenerate, the two worked-out eigenvectors are still automatically orthogonal to each other with respect to the inertia matrix. ? SAGE Publications.; EI; 3; 185-197; 44
语种	英语
内容类型	期刊论文
源URL	[http://ir.pku.edu.cn/handle/20.500.11897/494558]
专题	信息科学技术学院
推荐引用方式 GB/T 7714	Zhang, Gengmin. Finding out normal coordinates with the method of undetermined coefficients: An alternative starting point of solving a small oscillation problem with two degrees of freedom[J]. International Journal of Mechanical Engineering Education,2016.
APA	Zhang, Gengmin.(2016).Finding out normal coordinates with the method of undetermined coefficients: An alternative starting point of solving a small oscillation problem with two degrees of freedom.International Journal of Mechanical Engineering Education.
MLA	Zhang, Gengmin."Finding out normal coordinates with the method of undetermined coefficients: An alternative starting point of solving a small oscillation problem with two degrees of freedom".International Journal of Mechanical Engineering Education (2016).