4. Linear Integrals and Reduction

2018 ◽  
pp. 217-240
Keyword(s):  
Linear Integrals

Level manifolds of linear integrals in mechanical systems

2007 ◽  
Vol 62 (3) ◽  
pp. 69-75
Author(s):  
E. I. Kugushev ◽  
V. A. Mel’dianova
Keyword(s):  
Mechanical Systems ◽  
Linear Integrals

Two degree of freedom gyroscopic systems with linear integrals

Meccanica ◽  
2013 ◽  
Vol 49 (4) ◽  
pp. 973-979
Author(s):  
Ranislav M. Bulatovic ◽  
Mila Kazic
Keyword(s):  
Degree Of Freedom ◽  
Gyroscopic Systems ◽  
Two Degree Of Freedom ◽  
Linear Integrals

scholarly journals Aeronautical Inspirations in Biomechanics

2017 ◽  
Vol 24 (1) ◽  
pp. 5-9
Author(s):  
Ryszard Maroński
Keyword(s):  
Boundary Layer ◽  
Mathematical Models ◽  
Cancer Chemotherapy ◽  
Ballistic Missile ◽  
Minimum Time ◽  
Green’S Theorem ◽  
Aerospace Systems ◽  
Solution Methods ◽  
Problem Formulations ◽  
Linear Integrals

Abstract Introduction. The goal of the paper is to show that some problems formulated in the dynamics of atmospheric flight are very similar to the problems formulated in the biomechanics of motion and medicine. Three problems were compared: minimumheat transfer from the boundary layer to the ballistic missile skin, minimum-time ski descent, and the minimisation of the negative cumulated effect of the drug in cancer chemotherapy. Material and methods. All these problems are solved using the same method originally developed for aerospace systems - the method of Miele (the extremisation method of linear integrals via Green’s theorem). Results. It is shown that the problems arising in different branches of knowledge are very similar in problem formulations, mathematical models, and solution methods used. Conclusions. There are no barriers between different disciplines.

scholarly journals On Kilmister's Conditions for the Existence of Linear Integrals of Dynamical Systems

1965 ◽  
Vol 14 (3) ◽  
pp. 243-244 ◽  
Author(s):  
R. H. Boyer
Keyword(s):  
Dynamical Systems ◽  
Singular Integral ◽  
First Integral ◽  
Killing Field ◽  
Summation Convention ◽  
Covariant Derivation ◽  
Image Position ◽  
Generally Covariant ◽  
Linear Integrals

Kilmister (1) has considered dynamical systems specified by coordinates q( = 1, 2, , n) and a Lagrangian(with summation convention). He sought to determine generally covariant conditions for the existence of a first integral, , linear in the velocities. He showed that it is not, as is usually stated, necessary that there must exist an ignorable coordinate (equivalently, that b must be a Killing field:where covariant derivation is with respect to a). On the contrary, a singular integral, in the sense that for all time if satisfied initially, need not be accompanied by an ignorable coordinate.

scholarly journals Integrals of dynamical systems linear in the velocities

1971 ◽  
Vol 17 (3) ◽  
pp. 241-244
Author(s):  
C. D. Collinson
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Degrees Of Freedom ◽  
Integral Conditions ◽  
Two Degrees Of Freedom ◽  
Generalized Coordinates ◽  
Image Position ◽  
Linear Integrals

Kilmister (1) has discussed the existence of linear integrals of a dynamical system specified by generalized coordinates qα(α = 1, 2, …, n) and a Lagrangianrepeated indices being summed from 1 to n. He derived covariant conditions for the existence of such an integral, conditions which do not imply the existence of an ignorable coordinate. Boyer (2) discussed the conditions and found the most general Lagrangian satisfying the conditions for the case of two degrees of freedom (n = 2).

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