Premium
Ill‐Conditioned equations in kinematics and dynamics of machines
Author(s) -
Park Taewon,
Haug Edward J.
Publication year - 1988
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620260115
Subject(s) - kinematics , condition number , mathematics , gravitational singularity , matrix (chemical analysis) , algebraic number , algebraic equation , factorization , simple (philosophy) , algebra over a field , mathematical analysis , algorithm , nonlinear system , pure mathematics , classical mechanics , philosophy , eigenvalues and eigenvectors , physics , materials science , epistemology , quantum mechanics , composite material
During mechanical system kinematic and dynamic analysis, linear and non‐linear algebraic equations must be solved. Algebraic equations are often ill‐conditioned, due either to physical singularities or large numerical errors, in which case solutions may have large errors or analysis methods may fail. Causes of ill‐conditioned problems are studied and illustrated with examples. Ill‐conditioned matrices and matrix condition numbers are discussed and an efficient and reliable indicator of ill‐conditioned matrices is suggested. In constrained kinematic and dynamic analysis, equations are solved repetitively, so symbolic factorization is used. The ill‐conditioning problem due to symbolic factorization is discussed and methods of detecting ill‐conditioning are suggested. Three examples are studied to demonstrate the effectiveness and use of condition numbers and ill‐conditioned system detection methods.