Machine estimation of limits of applicability of S. A. Chaplygin's theorem
Authors:
Abstract
The theorem on differential inequalities of S. A. Chaplygin and its further generalizations give the possibility of evaluating the unknown solution of a differential equation by two comparison functions from above and below. This method is very effective for approximate determination of the motion trajectory of electromechanical systems or for estimation of additional motion caused by deviation of actual values of the system parameters from the calculated ones. However, the widespread use of methods based on the theorem of S. A. Chaplygin is hindered by difficulties in determining its limits of applicability.
Область исследования:
(Archived) Manufacturing machinery and equipment
References
- Chaplygin S. A. A new method of approximate integration of differential equations. STI, 1950.
- Azbelev N. V., Tsalyuk Z. B. About Chaplygin's problem. Ukr., Math. Journ. 1958. vol. X, No. 1.
- Aizerman M. A. Lectures on the Theory of Automatic Regulation. Fizmatgiz, 1958.
- Fikhtenholtz G. M. Course of Differential and Integral Calculus, vol. I, ed. III, GITTL, 1951.
- Shkolnikov A. D. Application of the theorem of S. A. Chaplygin to the estimation of the error of electromodeling. Journal of Mining Institute, 1961, vol. XLV, iss. 1.
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