Inverse problem of the calculus of variation, its application to integration of an ordinary non-linear second order differential equation

1990 ◽  
Vol 42 (3) ◽  
pp. 367-371
Author(s):  
M. M. Kabal'skii
Keyword(s):  
Differential Equation ◽  
Inverse Problem ◽  
Order Differential Equation ◽  
Second Order ◽  
Calculus Of Variation ◽  
Second Order Differential Equation ◽  
Non Linear

A Dynamic Model for Non-Linear Radial Forced Vibration of Unilateral Boring Tools and its Application to Improving the Accuracy of Boring Process

2012 ◽  
Vol 452-453 ◽  
pp. 124-128
Author(s):  
Peng Li ◽  
Li Zhi Gu
Keyword(s):  
Differential Equation ◽  
Dynamic Model ◽  
Forced Vibration ◽  
Order Differential Equation ◽  
Second Order ◽  
Factors Affecting ◽  
Second Order Differential Equation ◽  
Shock Absorbers ◽  
Non Linear ◽  
Elastic Shock

By analyzing factors affecting the accuracy of boring process on the precision boring machine, the article aims at putting forward a method of improving the accuracy of boring process by means of installing polymer elastic shock absorbers on unilateral boring tools. In addition, the situation of non-linear radial forced vibration is formulated by a dynamic model of second-order differential equation. Based on the model, vibration prevention principles of unilateral boring tools have been discussed and systematic parameters have been optimized for enhancement of the boring process accuracy.

On the integrability of solutions of perturbed non-linear differential equations

1977 ◽  
Vol 77 (3-4) ◽  
pp. 309-318 ◽  
Author(s):  
Paul W. Spikes
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Order Differential Equation ◽  
Sufficient Conditions ◽  
Second Order ◽  
Linear Differential Equations ◽  
Second Order Differential Equation ◽  
All Solutions ◽  
Non Linear ◽  
Linear Differential

SynopsisSufficient conditions are given to insure that all solutions of a perturbed non-linear second-order differential equation have certain integrability properties. In addition, some continuability and boundedness results are given for solutions of this equation.

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