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The Lagrangian and the Lie symmetries of charged particle motion in homogeneous electromagnetic field 被引量:2
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作者 楼智美 《Chinese Physics B》 SCIE EI CAS CSCD 2006年第5期891-894,共4页
In this paper, a constant of motion of charged particle motion in homogeneous electromagnetic field is derived from Newton's equations and the characteristics of partial differential equation, the related Lagrangian ... In this paper, a constant of motion of charged particle motion in homogeneous electromagnetic field is derived from Newton's equations and the characteristics of partial differential equation, the related Lagrangian is also given by means of the obtained constant of motion. By discussing the Lie symmetry for this classical system, this paper obtains the general expression of the conserved quantity, It is shown that the conserved quantity is the same as the constant of motion in essence, 展开更多
关键词 constant of motion LAGRANGIAN Lie symmetry conserved quantity
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Characteristic Functional Structure of Infinitesimal Symmetry Transformations for Nonholonomic System 被引量:1
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作者 张宏彬 陈立群 《Journal of Shanghai University(English Edition)》 CAS 2005年第2期134-138,共5页
It was proved that velocity-dependent infinitesima l symmetry transformations of nonholonomic systems have a characteristic functio nal structure, which could be formulated by means of an auxiliary symmetry tra nsform... It was proved that velocity-dependent infinitesima l symmetry transformations of nonholonomic systems have a characteristic functio nal structure, which could be formulated by means of an auxiliary symmetry tra nsformation function and is manifestly dependent upon constants of motion of th e system. An example was given to illustrate the applicability of the results. 展开更多
关键词 analytical mechanics nonholonomic system velocity-dependent infinitesimal symmetry transformation characteristic functional structure constant of motion.
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Quantization of the 1-D Forced Harmonic Oscillator in the Space (<i>x</i>, <i>v</i>)
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作者 Gustavo V. López Omar J. P. Bravo 《Journal of Modern Physics》 2021年第3期284-294,共11页
The quantization of the forced harmonic oscillator is studied with the quantum variable (<em>x</em>, <span style="white-space:nowrap;"><em><sub>v</sub><sup style="... The quantization of the forced harmonic oscillator is studied with the quantum variable (<em>x</em>, <span style="white-space:nowrap;"><em><sub>v</sub><sup style="margin-left:-8px;">∧</sup></em></span>), with the commutation relation <img src="Edit_28f5b839-7de4-41e5-9ed8-69dc1bf72c2c.bmp" alt="" />, and using a Schr<span style="white-space:nowrap;"><span style="white-space:nowrap;"><span style="white-space:nowrap;">&ouml;</span></span></span>dinger’s like equation on these variable, and associating a linear operator to a constant of motion <em>K</em> (<em>x, v, t</em>) of the classical system, The comparison with the quantization in the space (<em>x, p</em>) is done with the usual Schr<span style="white-space:nowrap;"><span style="white-space:nowrap;"><span style="white-space:nowrap;">&ouml;</span></span></span>dinger’s equation for the Hamiltonian <em>H</em><span style="white-space:normal;">(</span><em style="white-space:normal;">x, p, t</em><span style="white-space:normal;">)</span>, and with the commutation relation <img src="Edit_cca7e318-5b35-4c55-8f09-6089970ce9a2.bmp" alt="" />. It is found that for the non-resonant case, both forms of quantization bring about the same result. However, for the resonant case, both forms of quantization are different, and the probability for the system to be in the exited state for the (<em style="white-space:normal;">x</em><span style="white-space:normal;">, </span><em><sub>v</sub><sup style="margin-left:-8px;">∧</sup></em>) quantization has fewer oscillations than the (<em style="white-space:normal;">x</em><span style="white-space:normal;">, </span><em style="white-space:normal;"><sub>p</sub><sup style="margin-left:-8px;">∧</sup></em>) quantization, the average energy of the system is higher in (<em style="white-space:normal;">x</em><span style="white-space:normal;">, </span><em style="white-space:normal;"><sub>p</sub><sup style="margin-left:-8px;">∧</sup></em>) quantization than on the (<em style="white-space:normal;">x</em><span style="white-space:normal;">, </span><em style="white-space:normal;"><sub>v</sub><sup style="margin-left:-8px;">∧</sup></em>) quantization, and the Boltzmann-Shannon entropy on the (<em style="white-space:normal;">x</em><span style="white-space:normal;">, </span><em style="white-space:normal;"><sub>p</sub><sup style="margin-left:-8px;">∧</sup></em>) quantization is higher than on the (<em style="white-space:normal;">x</em><span style="white-space:normal;">, </span><em style="white-space:normal;"><sub>v</sub><sup style="margin-left:-8px;">∧</sup></em>) quantization. 展开更多
关键词 Forced Harmonic Oscillator (x v style="margin-left:-8px ">∧) Quantization constant of motion
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A New Formulation of Classical Mechanics—Part 1
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作者 Federico Petrovich 《Journal of Applied Mathematics and Physics》 2016年第2期412-431,共20页
This paper has two parts, in this occasion we will present the first one. Until today, there are two formulations of classical mechanics. The first one is based on the Newton’s laws and the second one is based on the... This paper has two parts, in this occasion we will present the first one. Until today, there are two formulations of classical mechanics. The first one is based on the Newton’s laws and the second one is based on the principle of least action. In this paper, we will find a third formulation that is totally different and has some advantages in comparison with the other two formulations. 展开更多
关键词 Classical Mechanics constant of motion DISSIPATION
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One Dimensional Conservative System with Quadratic Dissipation and Position Depending Mass
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作者 Gustavo V. López Erick S. Madrigal 《Journal of Modern Physics》 2022年第2期127-137,共11页
Forl a 1-D conservative system with a position depending mass within a dissipative medium, its effect on the body is to exert a force depending on the squared of its velocity, a constant of motion, Lagrangian, general... Forl a 1-D conservative system with a position depending mass within a dissipative medium, its effect on the body is to exert a force depending on the squared of its velocity, a constant of motion, Lagrangian, generalized linear momentum, and Hamiltonian are obtained. We apply these new results to the harmonic oscillator and pendulum under the characteristics mentioned about, obtaining their constant of motion, Lagrangian and Hamiltonian for the case when the body is increasing its mass. 展开更多
关键词 DISSIPATION Position Mass Depending constant of motion HAMILTONIAN
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Deformed oscillator algebra for quantum superintegrable systems in two-dimensional Euclidean space and on a complex two-sphere
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作者 H.Panahi Z.Alizadeh 《Chinese Physics B》 SCIE EI CAS CSCD 2013年第6期175-180,共6页
In this work, we study superintegrable quantum systems in two-dimensional Euclidean space and on a complex twosphere with second-order constants of motion. We show that these constants of motion satisfy the deformed o... In this work, we study superintegrable quantum systems in two-dimensional Euclidean space and on a complex twosphere with second-order constants of motion. We show that these constants of motion satisfy the deformed oscillator algebra. Then, we easily calculate the energy eigenvalues in an algebraic way by solving of a system of two equations satisfied by its structure function. The results are in agreement to the ones obtained from the solution of the relevant Schroedinger equation. 展开更多
关键词 superintegrable systems constants of motion deformed oscillator algebra structure function
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