Connection of optimum temporal exponents with a principle of least action

E. V. Sergeev; A. V. Karzanov; A. V. Tremaskin

doi:10.1117/12.804374

5 June 2008 Connection of optimum temporal exponents with a principle of least action

E. V. Sergeev, A. V. Karzanov, A. V. Tremaskin

Proceedings Volume 7121, Eighth Seminar on Problems of Theoretical and Applied Electron and Ion Optics; 712109 (2008) https://doi.org/10.1117/12.804374
Event: Eighth Seminar on Problems of Theoretical and Applied Electron and Ion Optics, 2007, Moscow, Russian Federation

Abstract

The principle of the least action states, that the motion of objects on optimum trajectories conjugates to the underload expenditure of activity. In the canonical approach this statement is reduced to searching extreme activity. For the immediate proof of the underload expenditure of activity on optimum trajectories the relevant mathematical algorithm in the basis of which bottom the concept of optimum time exponents lays is offered. Using this algorithm, various modes of a motion of charged particles are explored: the harmonic motion, a motion in the homogeneous force field, a motion in a central force field and a motion on inertia. The terrain clearance minimum under the rate of flux of activity for the harmonic motions is detected.

Citation Download Citation

E. V. Sergeev, A. V. Karzanov, and A. V. Tremaskin "Connection of optimum temporal exponents with a principle of least action", Proc. SPIE 7121, Eighth Seminar on Problems of Theoretical and Applied Electron and Ion Optics, 712109 (5 June 2008); https://doi.org/10.1117/12.804374

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