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| Format: | Artículo científico |
| Language: | en |
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Sociedade Brasileira de Física
2006
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| Online Access: | https://www.redalyc.org/articulo.oa?id=46436624 |
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| _version_ | 1866585451046895616 |
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| author | R. C. Santos |
| author_facet | R. C. Santos |
| contents | Hamilton-Jacobi Approach for Power-Law Potentials R. C. Santos J. Santos J. A. S. Lima Física, Astronomía y Matemáticas Power Hamilton law potentials Jacobi equation The classical and relativistic Hamilton-Jacobi approach is applied to the one-dimensional homogeneous potential,V(q) = αqn, where α and n are continuously varying parameters. In the non-relativistic case, the exactanalytical solution is determined in terms of α, n and the total energy E. It is also shown that the non-linearequation of motion can be linearized by constructing a hypergeometric differential equation for the inverse problemt(q). A variable transformation reducing the general problem to that one of a particle subjected to a linearforce is also established. For any value of n, it leads to a simple harmonic oscillator if E > 0, an anti-oscillatorif E < 0, or a free particle if E = 0. However, such a reduction is not possible in the relativistic case. For abounded relativistic motion, the first order correction to the period is determined for any value of n. For n >> 1,it is found that the correction is just twice that one deduced for the simple harmonic oscillator (n = 2), and doesnot depend on the specific value of n. 2006 artículo científico 0103-9733 https://www.redalyc.org/articulo.oa?id=46436624 en http://www.redalyc.org/revista.oa?id=464 Brazilian Journal of Physics application/pdf Sociedade Brasileira de Física Brazilian Journal of Physics (Brasil) Num.4A Vol.36 |
| format | Artículo científico |
| id | redalyc_46436624 |
| language | en |
| publishDate | 2006 |
| publisher | Sociedade Brasileira de Física |
| spellingShingle | Hamilton-Jacobi Approach for Power-Law Potentials R. C. Santos Física, Astronomía y Matemáticas Power Hamilton law potentials Jacobi equation Hamilton-Jacobi Approach for Power-Law Potentials R. C. Santos J. Santos J. A. S. Lima Física, Astronomía y Matemáticas Power Hamilton law potentials Jacobi equation The classical and relativistic Hamilton-Jacobi approach is applied to the one-dimensional homogeneous potential,V(q) = αqn, where α and n are continuously varying parameters. In the non-relativistic case, the exactanalytical solution is determined in terms of α, n and the total energy E. It is also shown that the non-linearequation of motion can be linearized by constructing a hypergeometric differential equation for the inverse problemt(q). A variable transformation reducing the general problem to that one of a particle subjected to a linearforce is also established. For any value of n, it leads to a simple harmonic oscillator if E > 0, an anti-oscillatorif E < 0, or a free particle if E = 0. However, such a reduction is not possible in the relativistic case. For abounded relativistic motion, the first order correction to the period is determined for any value of n. For n >> 1,it is found that the correction is just twice that one deduced for the simple harmonic oscillator (n = 2), and doesnot depend on the specific value of n. 2006 artículo científico 0103-9733 https://www.redalyc.org/articulo.oa?id=46436624 en http://www.redalyc.org/revista.oa?id=464 Brazilian Journal of Physics application/pdf Sociedade Brasileira de Física Brazilian Journal of Physics (Brasil) Num.4A Vol.36 |
| title | Hamilton-Jacobi Approach for Power-Law Potentials |
| topic | Física, Astronomía y Matemáticas Power Hamilton law potentials Jacobi equation |
| url | https://www.redalyc.org/articulo.oa?id=46436624 |