Differentiable and Complex Dynamics of Several Variables:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht
Springer Netherlands
1999
|
| Schriftenreihe: | Mathematics and Its Applications
483 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | The development of dynamics theory began with the work of Isaac Newton. In his theory the most basic law of classical mechanics is f = ma, which describes the motion n in IR. of a point of mass m under the action of a force f by giving the acceleration a. If n the position of the point is taken to be a point x E IR. , and if the force f is supposed to be a function of x only, Newton's Law is a description in terms of a second-order ordinary differential equation: J2x m dt = f(x). 2 It makes sense to reduce the equations to first order by defining the velo city as an extra n independent variable by v = :i; = ~~ E IR. . Then x = v, mv = f(x). L. Euler, J. L. Lagrange and others studied mechanics by means of an analytical method called analytical dynamics. Whenever the force f is represented by a gradient vector field f = - \lU of the potential energy U, and denotes the difference of the kinetic energy and the potential energy by 1 L(x,v) = 2'm(v,v) - U(x), the Newton equation of motion is reduced to the Euler-Lagrange equation ~~ are used as the variables, the Euler-Lagrange equation can be If the momenta y written as . 8L y= 8x' Further, W. R. |
| Beschreibung: | 1 Online-Ressource (X, 342 p) |
| ISBN: | 9789401592994 9789048152469 |
| DOI: | 10.1007/978-94-015-9299-4 |
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| 500 | |a The development of dynamics theory began with the work of Isaac Newton. In his theory the most basic law of classical mechanics is f = ma, which describes the motion n in IR. of a point of mass m under the action of a force f by giving the acceleration a. If n the position of the point is taken to be a point x E IR. , and if the force f is supposed to be a function of x only, Newton's Law is a description in terms of a second-order ordinary differential equation: J2x m dt = f(x). 2 It makes sense to reduce the equations to first order by defining the velo city as an extra n independent variable by v = :i; = ~~ E IR. . Then x = v, mv = f(x). L. Euler, J. L. Lagrange and others studied mechanics by means of an analytical method called analytical dynamics. Whenever the force f is represented by a gradient vector field f = - \lU of the potential energy U, and denotes the difference of the kinetic energy and the potential energy by 1 L(x,v) = 2'm(v,v) - U(x), the Newton equation of motion is reduced to the Euler-Lagrange equation ~~ are used as the variables, the Euler-Lagrange equation can be If the momenta y written as . 8L y= 8x' Further, W. R. | ||
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| indexdate | 2024-07-10T01:21:14Z |
| institution | BVB |
| isbn | 9789401592994 9789048152469 |
| language | English |
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| spelling | Hu, Pei-Chu Verfasser aut Differentiable and Complex Dynamics of Several Variables by Pei-Chu Hu, Chung-Chun Yang Dordrecht Springer Netherlands 1999 1 Online-Ressource (X, 342 p) txt rdacontent c rdamedia cr rdacarrier Mathematics and Its Applications 483 The development of dynamics theory began with the work of Isaac Newton. In his theory the most basic law of classical mechanics is f = ma, which describes the motion n in IR. of a point of mass m under the action of a force f by giving the acceleration a. If n the position of the point is taken to be a point x E IR. , and if the force f is supposed to be a function of x only, Newton's Law is a description in terms of a second-order ordinary differential equation: J2x m dt = f(x). 2 It makes sense to reduce the equations to first order by defining the velo city as an extra n independent variable by v = :i; = ~~ E IR. . Then x = v, mv = f(x). L. Euler, J. L. Lagrange and others studied mechanics by means of an analytical method called analytical dynamics. Whenever the force f is represented by a gradient vector field f = - \lU of the potential energy U, and denotes the difference of the kinetic energy and the potential energy by 1 L(x,v) = 2'm(v,v) - U(x), the Newton equation of motion is reduced to the Euler-Lagrange equation ~~ are used as the variables, the Euler-Lagrange equation can be If the momenta y written as . 8L y= 8x' Further, W. R. Mathematics Global analysis Differential equations, partial Global differential geometry Global Analysis and Analysis on Manifolds Several Complex Variables and Analytic Spaces Partial Differential Equations Differential Geometry Measure and Integration Mathematik Differenzierbares dynamisches System (DE-588)4137931-7 gnd rswk-swf Mehrere komplexe Variable (DE-588)4169285-8 gnd rswk-swf Differenzierbares dynamisches System (DE-588)4137931-7 s Mehrere komplexe Variable (DE-588)4169285-8 s 1\p DE-604 Yang, Chung-Chun Sonstige oth https://doi.org/10.1007/978-94-015-9299-4 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Hu, Pei-Chu Differentiable and Complex Dynamics of Several Variables Mathematics Global analysis Differential equations, partial Global differential geometry Global Analysis and Analysis on Manifolds Several Complex Variables and Analytic Spaces Partial Differential Equations Differential Geometry Measure and Integration Mathematik Differenzierbares dynamisches System (DE-588)4137931-7 gnd Mehrere komplexe Variable (DE-588)4169285-8 gnd |
| subject_GND | (DE-588)4137931-7 (DE-588)4169285-8 |
| title | Differentiable and Complex Dynamics of Several Variables |
| title_auth | Differentiable and Complex Dynamics of Several Variables |
| title_exact_search | Differentiable and Complex Dynamics of Several Variables |
| title_full | Differentiable and Complex Dynamics of Several Variables by Pei-Chu Hu, Chung-Chun Yang |
| title_fullStr | Differentiable and Complex Dynamics of Several Variables by Pei-Chu Hu, Chung-Chun Yang |
| title_full_unstemmed | Differentiable and Complex Dynamics of Several Variables by Pei-Chu Hu, Chung-Chun Yang |
| title_short | Differentiable and Complex Dynamics of Several Variables |
| title_sort | differentiable and complex dynamics of several variables |
| topic | Mathematics Global analysis Differential equations, partial Global differential geometry Global Analysis and Analysis on Manifolds Several Complex Variables and Analytic Spaces Partial Differential Equations Differential Geometry Measure and Integration Mathematik Differenzierbares dynamisches System (DE-588)4137931-7 gnd Mehrere komplexe Variable (DE-588)4169285-8 gnd |
| topic_facet | Mathematics Global analysis Differential equations, partial Global differential geometry Global Analysis and Analysis on Manifolds Several Complex Variables and Analytic Spaces Partial Differential Equations Differential Geometry Measure and Integration Mathematik Differenzierbares dynamisches System Mehrere komplexe Variable |
| url | https://doi.org/10.1007/978-94-015-9299-4 |
| work_keys_str_mv | AT hupeichu differentiableandcomplexdynamicsofseveralvariables AT yangchungchun differentiableandcomplexdynamicsofseveralvariables |