Integration of Linear Equations of Motion

by Robert J. Melosh, (A.M.ASCE), Engr. and Mgr.; Marc Analysis Research Corp., Palo Alto, Calif.; formerly, Section Supervisor, Virginia Polytechnic Inst. and State Univ., Blacksburg, Va.,

Serial Information: Journal of the Structural Division, 1975, Vol. 101, Issue 7, Pg. 1551-1558

Document Type: Journal Paper


This paper presents features of implementation of a transfer algorithm for solving linear ordinary differential equations using a digital computer. It shows results of applications to simple problems. Tests show the algorithm requires less computer time per step than other representative direct methods. It does not need adaptive error control. Variable time step logic is not required for integration to be efficient and effective. The consequences of these advantages are evidence in reducing computer times for Runge-Kutta integration by a factor of 4,000 while obtaining answers of improved accuracy. The examination shows that the efficiency and accuracy of the algorithm dictate use of an integration step size of the order of one-fifth the time of the shortest system period represented. The relation between the period and the number of calculations to generate the transfer matrix provides a reliable means of insuring that the appropriate time step is being used.

Subject Headings: Equations of motion | Algorithms | Computing in civil engineering | Linear functions | Differential equations | Adaptive systems | Matrix (mathematics)

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