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This chapter introduces analytical solutions for SCL design, highlighting their role in early-stage analysis, rapid sensitivity checks, and validation of numerical models. It explains benefits, limitations, and applications for simple geometries and ground conditions.
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An Analytical Solution of the Inverted Pendulum
American Journal of Physics, 1965A rigorous solution of the inverted pendulum requires several mathematical techniques which are not in the repetoire of the typical student of classical mechanics at the senior level. However, the problem is tractable by Lagrange's equations and the physics of the situation is sufficiently simple so that it is an excellent example to use to extend the ...
Phelps, F. M. III, Hunter, J. H. jun.
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An Analytic Solution of the Warehouse Problem
Management Science, 1957In a recent paper, [Bellman, Richard. 1956. On the theory of dynamic programming—a warehousing problem. Management Sci. 2 (3, April) 272.], Bellman uses dynamic programming to establish a computational algorithm for the solution of the “warehouse” problem.
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