Notes for AKT-140110/0:35:38 - Revision history

Leo algknt at 19:57, 25 May 2018

2018-05-25T19:57:25Z

← Older revision		Revision as of 15:57, 25 May 2018
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	'''Lagrangian Mechanics''' is a tool used in studying motions in Classical Mechanics and it was introduced by Joseph-Louis Lagrange in 1788. An important concept in Lagragian Mechanics is that the equations of motion of Classical Mechanics can be based on a variational principle, namely, that along a path describing classical motion the '''action integral''' assumes a minimal value (Hamiltonian Principle of Least Action)		'''Lagrangian Mechanics''' is a tool used in studying motions in Classical Mechanics and it was introduced by Joseph-Louis Lagrange in 1788. An important concept in Lagragian Mechanics is that the equations of motion of Classical Mechanics can be based on a variational principle, namely, that along a path describing classical motion the '''action integral''' assumes a minimal value (Hamiltonian Principle of Least Action)

	The action integral is given by <math>S[x(t)] = \int^{t_1}_{t_0} dt \mathcal{L}(x(t),,t)</math>, where <math>\mathcal{L}(x(t),~~\.{~~x(t)},t) = \frac12 \.{x(t)}^2-U(x(t))/math> is called the Lagrangian.		The action integral is given by <math>S[x(t)] = \int^{t_1}_{t_0} dt \mathcal{L}(x(t),x^\prime(t),t)</math>, where <math>\mathcal{L}(x(t),x^\prime(t),t) = \frac12 {x^\prime(t)}^2-U(x(t))</math> is called the Lagrangian.

Leo algknt at 19:52, 25 May 2018

2018-05-25T19:52:27Z

← Older revision		Revision as of 15:52, 25 May 2018
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	'''Lagrangian Mechanics''' is a tool used in studying motions in Classical Mechanics and it was introduced by Joseph-Louis Lagrange in 1788. An important concept in Lagragian Mechanics is that the equations of motion of Classical Mechanics can be based on a variational principle, namely, that along a path describing classical motion the '''action integral''' assumes a minimal value (Hamiltonian Principle of Least Action)		'''Lagrangian Mechanics''' is a tool used in studying motions in Classical Mechanics and it was introduced by Joseph-Louis Lagrange in 1788. An important concept in Lagragian Mechanics is that the equations of motion of Classical Mechanics can be based on a variational principle, namely, that along a path describing classical motion the '''action integral''' assumes a minimal value (Hamiltonian Principle of Least Action)

	The action integral is given by <math>S[x(t)] = \int^{t_1}_{t_0} dt \mathcal{L}(x(t),~~\.{x(t)}~~,t)</math>, where <math>\mathcal{L}(x(t),\.{x(t)},t) = \frac12 \.{x(t)}^2-U(x(t))/math> is called the Lagrangian.		The action integral is given by <math>S[x(t)] = \int^{t_1}_{t_0} dt \mathcal{L}(x(t),,t)</math>, where <math>\mathcal{L}(x(t),\.{x(t)},t) = \frac12 \.{x(t)}^2-U(x(t))/math> is called the Lagrangian.

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2018-05-25T19:48:40Z

Created page with "'''Lagrangian Mechanics''' is a tool used in studying motions in Classical Mechanics and it was introduced by Joseph-Louis Lagrange in 1788. An important concept in Lagragian ..."

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'''Lagrangian Mechanics''' is a tool used in studying motions in Classical Mechanics and it was introduced by Joseph-Louis Lagrange in 1788. An important concept in Lagragian Mechanics is that the equations of motion of Classical Mechanics can be based on a variational principle, namely, that along a path describing classical motion the '''action integral''' assumes a minimal value (Hamiltonian Principle of Least Action)

The action integral is given by <math>S[x(t)] = \int^{t_1}_{t_0} dt \mathcal{L}(x(t),\.{x(t)},t)</math>, where <math>\mathcal{L}(x(t),\.{x(t)},t) = \frac12 \.{x(t)}^2-U(x(t))/math> is called the Lagrangian.