theories:classical_mechanics:lagrangian
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theories:classical_mechanics:lagrangian [2018/05/06 11:31] jakobadmin [Concrete] |
theories:classical_mechanics:lagrangian [2018/10/11 14:12] (current) jakobadmin [Abstract] |
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| \end{equation} | \end{equation} | ||
| - | [{{ :theories:trajectories.png?nolink&400|Source: Lectures on Classical Mechanics by [[http://math.ucr.edu/home/baez/classical/texfiles/2005/book/classical.pdf|John C. Baez]]}}] | + | {{ :theories:classical_mechanics:lagrangianpfad.png?nolink&400|}} |
| The basic idea is now that nature causes | The basic idea is now that nature causes | ||
| particles to follow the trajectories with the //least// amount of action. | particles to follow the trajectories with the //least// amount of action. | ||
| - | In the image on the right-hand side this could be the solid line denotes by $q$. Another path is shown as a dashed line and denoted by $q(s)$. The Lagrangian approach assigns to each path a quantity called action as defined above and then tells us that the correct path that an object really follows is the path with minimal action. In our example the path $q$ could have an action of $3$ and the path $q_s$ an action of $5$. Hence, path $q$ is correct and not path $q_s$. | + | In the image on the right-hand side this could be the solid line denotes by $q$. Another path is shown as a dashed line and denoted by $q(s)$. |
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| + | The Lagrangian approach assigns to each path a quantity called action as defined above and then tells us that the correct path that an object really follows is the path with minimal action. In our example the path $q$ could have an action of $3$ and the path $q_s$ an action of $5$. Hence, path $q$ is correct and not path $q_s$. | ||
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| * The best book on Lagrangian mechanics is The Lazy Universe by Coopersmith | * The best book on Lagrangian mechanics is The Lazy Universe by Coopersmith | ||
| + | * Many problems with solutions are collected in [[https://archive.org/details/SchaumsTheoryAndProblemsOfTheoreticalMechanics|Schaum's Outline of Theory and Problems of Theoretical Mechanics]] by Murray R Spiegel | ||
| <tabbox Abstract> | <tabbox Abstract> | ||
| Lagrangian mechanics can be formulated geometrically using [[advanced_tools:fiber_bundles|fibre bundles]]. | Lagrangian mechanics can be formulated geometrically using [[advanced_tools:fiber_bundles|fibre bundles]]. | ||
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| ---- | ---- | ||
| + | * [[https://core.ac.uk/download/pdf/4887416.pdf|Lectures on Mechanics]] by Marsden | ||
| * See page 471 in Road to Reality by R. Penrose, page 167 in Geometric Methods of Mathematical Physics by B. Schutz and http://philsci-archive.pitt.edu/2362/1/Part1ButterfForBub.pdf. | * See page 471 in Road to Reality by R. Penrose, page 167 in Geometric Methods of Mathematical Physics by B. Schutz and http://philsci-archive.pitt.edu/2362/1/Part1ButterfForBub.pdf. | ||
theories/classical_mechanics/lagrangian.1525599118.txt.gz · Last modified: 2018/05/06 09:31 (external edit)
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