- published: 15 May 2009
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Hamilton may refer to:
Hamiltonian mechanics is a theory developed as a reformulation of classical mechanics and predicts the same outcomes as non-Hamiltonian classical mechanics. It uses a different mathematical formalism, providing a more abstract understanding of the theory. Historically, it was an important reformulation of classical mechanics, which later contributed to the formulation of statistical mechanics and quantum mechanics.
Hamiltonian mechanics was first formulated by William Rowan Hamilton in 1833, starting from Lagrangian mechanics, a previous reformulation of classical mechanics introduced by Joseph Louis Lagrange in 1788.
In Hamiltonian mechanics, a classical physical system is described by a set of canonical coordinates , where each component of the coordinate is indexed to the frame of reference of the system.
The time evolution of the system is uniquely defined by Hamilton's equations:
where is the Hamiltonian, which often corresponds to the total energy of the system. For a closed system, it is the sum of the kinetic and potential energy in the system.
In physics, classical mechanics and quantum mechanics are the two major sub-fields of mechanics. Classical mechanics is concerned with the set of physical laws describing the motion of bodies under the influence of a system of forces. The study of the motion of bodies is an ancient one, making classical mechanics one of the oldest and largest subjects in science, engineering and technology. It is also widely known as Newtonian mechanics.
Classical mechanics describes the motion of macroscopic objects, from projectiles to parts of machinery, as well as astronomical objects, such as spacecraft, planets, stars, and galaxies. Within classical mechanics are fields of study that describe the behavior of solids, liquids and gases and other specific sub-topics. Classical mechanics also provides extremely accurate results as long as the domain of study is restricted to large objects and the speeds involved do not approach the speed of light. When the objects being dealt with become sufficiently small, it becomes necessary to introduce the other major sub-field of mechanics, quantum mechanics, which adjusts the laws of physics of macroscopic objects for the atomic nature of matter by including the wave–particle duality of atoms and molecules. When both quantum mechanics and classical mechanics cannot apply, such as at the quantum level with high speeds, quantum field theory (QFT) becomes applicable.
Every object experiences some form of motion which is the result of different forces acting on the object. Dynamics is the study of the forces which are responsible for this motion. Dynamics (from Greek δυναμικός dynamikos "powerful", from δύναμις dynamis "power") may refer to:
Coordinates: 12°59′29″N 80°14′01″E / 12.99151°N 80.23362°E / 12.99151; 80.23362
The Indian Institute of Technology Madras (Tamil: இந்திய தொழில்நுட்பக் கழகம், மெட்ராஸ்) is an autonomous public engineering and research institution located in Chennai (formerly Madras), Tamil Nadu, India. It is recognised as an Institute of National Importance by the Government of India. Founded in 1959 with technical and financial assistance from the former government of West Germany, it was the third Indian Institute of Technology that was established by the Government of India through an Act of Parliament, to provide education and research facilities in engineering and technology.
IIT Madras is a residential institute that occupies a 2.5 km² campus that was formerly part of the adjoining Guindy National Park. The institute has nearly 550 faculty, 8,000 students and 1,250 administrative and supporting staff. Growing ever since it obtained its charter from the Indian Parliament in 1961, much of the campus is a protected forest, carved out of the Guindy National Park, home to large numbers of chital (spotted deer), black buck, monkeys, and other rare wildlife. A natural lake, deepened in 1988 and 2003, drains most of its rainwater.
Lecture Series on Classical Physics by Prof.V.Balakrishnan, Department of Physics, IIT Madras. For more details on NPTEL visit http://nptel.iitm.ac.in
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain what is Hamiltonian mechanics, how are the equations derived, how the Hamiltonian equations will simplified into classical mechanics equations. Next video in this series can be seen at: https://youtu.be/-VXDbFELld8
Topics in Nonlinear Dynamics by Prof. V. Balakrishnan,Department of Physics,IIT Madras.For more details on NPTEL visit http://nptel.ac.in
A different way to understand classical Hamiltonian mechanics in terms of determinism and reversibility. See all videos in the series: Playlist - https://www.youtube.com/playlist?list=PLmNMSMaNjnDd9Qj4VxNL8dijiWZCAzanl 1. Math - https://www.youtube.com/watch?v=FGQddvjP19w 2. Measurements - https://www.youtube.com/watch?v=UTSJiYV4rmw 3. Thermodynamics - https://www.youtube.com/watch?v=hb4nDn0CR7Q 4. Information Theory - https://www.youtube.com/watch?v=6vPIVJ-LtOI 5. State Mapping - https://www.youtube.com/watch?v=us0QK9xTN3o 6. Multiple d.o.f - https://www.youtube.com/watch?v=xJIglyPvCT0 7. Multiple d.o.f reprise - https://www.youtube.com/watch?v=wQBiUrQ3Va0
(November 7, 2011) Leonard Susskind discusses the some of the basic laws and ideas of modern physics. In this lecture, he focuses on Liouville's Theorem, which he describes as one of the basis for Hamiltonian mechanics. He works to prove the reversibility of classical mechanics. This course is the beginning of a six course sequence that explores the theoretical foundations of modern physics. Topics in the series include classical mechanics, quantum mechanics, theories of relativity, electromagnetism, cosmology, and black holes. Stanford University http://www.stanford.edu/ Stanford Continuing Studies http:/continuingstudies.stanford.edu/ Stanford University Channel on YouTube: http://www.youtube.com/stanford
Jacob Linder: 26.01.2012, Classical Mechanics (TFY4345), V2012 NTNU A full textbook covering the material in the lectures in detail can be downloaded for free here: http://bookboon.com/en/introduction-to-lagrangian-hamiltonian-mechanics-ebook
Alvaro Pelayo Member, School of Mathematics April 4, 2011 I will start with a review the basic notions of Hamiltonian/symplectic vector field and of Hamiltonian/symplectic group action, and the classical structure theorems of Kostant, Atiyah, Guillemin-Sternberg and Delzant on Hamiltonian torus actions. Then I will state a structure theorem for general symplectic torus actions, and give an idea of its proof. In the second part of the talk I will introduce new symplectic invariants of completely integrable Hamiltonian systems in low dimensions, and explain how these invariants determine, up to isomorphisms, the so called "semitoric systems". Semitoric systems are Hamiltonian systems which lie somewhere between the more rigid toric systems and the usually complicated general integrable syste...
MIT 2.003SC Engineering Dynamics, Fall 2011 View the complete course: http://ocw.mit.edu/2-003SCF11 Instructor: J. Kim Vandiver License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
Daniel Sutton: An effective description of Hamiltonian dynamics via the Maupertuis principle We study effective descriptions for the motion of a particle moving in a bounded periodic potential, as governed by Newton's second law. In particular we seek an effective equation, describing the motion of the particle in a rapidly oscillating potential. The study of such problems was initiated by P. L. Lions, G. Papanicolaou and S. R. S. Varadhan (1987) through the homogenisation of the Hamilton-Jacobi PDE. We propose an alternative approach, that is to use the principle of Maupertuis (1744). In this alternative formulation, which characterises dynamical trajectories as geodesics in a Riemannian manifold, we are able to describe properties of effective Hamiltonians in certain cases; specifically...
I created this video with the YouTube Video Editor (http://www.youtube.com/editor)
http://wd-central.com - Roger Hamilton talks about the Wealth Dynamics, the profiling system that lets you find out exactly who you are and how you should be working with others around you. The Wealth Dynamics Profiling system provides clarity on your path of least resistance to wealth creation. Through a profiling test it identifies your specific path to wealth. Wealth Dynamics is an evolution of Jungian psychometric testing into specific action & thinking dynamics that relates to entrepreneurs. It goes back to the roots of personality profiling in Chinese philosophy, which precedes Western psychometric testing by 2,500 years. Rather than just being a profiling report and list of soft recommendations, Wealth Dynamics provides an intuitive system which equips an entrepreneur with: 1. ...
Visit http://ilectureonline.com for more math and science lectures! In this video I will find the equations of a simple oscillator of a mass attached to a spring using the Hamiltonian equations. Next video in this series can be seen at: https://youtu.be/ziYJ6jQG8q8
Princeton/IAS Symplectic Geometry Seminar Topic:C0C0 Hamiltonian dynamics and a counterexample to the Arnold conjecture Speaker: Sobhan Seyfaddini Affiliation: Member, School of Mathematics Date: November 29, 2016 For more videos, visit http://video.ias.edu
Doris Hein Institute for Advanced Study; Member, School of Mathematics September 25, 2013 For more videos, visit http://video.ias.edu
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain what is, when to use, and why do we need Lagrangian mechanics. Next video in this series can be seen at: https://youtu.be/uFnTRJ2be7I
Lecture 16 of my Classical Mechanics course at McGill University, Winter 2010. Hamiltonian Mechanics. Phase Space. The course webpage, including links to other lectures and problem sets, is available at http://www.physics.mcgill.ca/~maloney/451/ The written notes for this lecture are available at http://www.physics.mcgill.ca/~maloney/451/451-16.pdf
Visit http://ilectureonline.com for more math and science lectures! In this video I will derive the position with-respect-to time and frequency equation of a simple pendulum problem using the partial derivative of Lagrangian equation. Next video in this series can be seen at: https://youtu.be/KCKbOVioirg
Lecture Series on Classical Physics by Prof.V.Balakrishnan, Department of Physics, IIT Madras. For more details on NPTEL visit http://nptel.iitm.ac.in
In this lecture you will learn: Introduction to Hamiltonian dynamics. Made by: Department of Physics, IIT Madras. This video is part of the playlist "University Lectures". For further interesting topics you can look here: https://www.youtube.com/playlist?list=PLdId9dvaMGZPorXrqBHGYn788r1vjVkXl "Hamiltonian mechanics is a theory developed as a reformulation of classical mechanics and predicts the same outcomes as non-Hamiltonian classical mechanics." https://en.wikipedia.org/wiki/Hamiltonian_mechanics This video was made by another YouTube user and made available for the use under the Creative Commons licence "CC-BY". Source channel: https://www.youtube.com/user/nptelhrd
iTunes / Apple Music: http://bit.ly/DynamicsofSalutation iTunes / Apple Music: http://bit.ly/DynamicsofSalutation iTunes / Apple Music: http://bit.ly/DynamicsofSalutation
Advanced dynamics is about modelling complex mechanical systems and assessing how their equations of motion can be derived. In the online course Advanced Dynamics, that follows Lagrangian Mechanics, you learn to derive the equation of motion of a dynamic system. The course will cover various topics including: *Momentum and Angular Momentum *Kinetic energy *Potential energy *3D mechanics appropriate for symbolic manipulation *Lagrange equation of motion *Gyroscopic Motion *Matrix notation for vectors, vector transformation and vector multiplications, transformation matrix, rotation operator, inertia matrix *Kinetic energy of bodies with a fixed point in space *Equations of motion of bodies with a fixed point in space (3D) *Equations of motion of free bodies *Hamilton's Principle *Simu...
Lecture Series on Classical Physics by Prof.V.Balakrishnan, Department of Physics, IIT Madras. For more details on NPTEL visit http://nptel.iitm.ac.in
Periodic Orbits in Hamiltonian Dynamics Doris Hein University of California, Santa Cruz; Member, School of Mathematics September 28, 2012
Lecture Series on Classical Physics by Prof.V.Balakrishnan, Department of Physics, IIT Madras. For more details on NPTEL visit http://nptel.iitm.ac.in
Topics in Nonlinear Dynamics by Prof. V. Balakrishnan,Department of Physics,IIT Madras.For more details on NPTEL visit http://nptel.ac.in
(November 7, 2011) Leonard Susskind discusses the some of the basic laws and ideas of modern physics. In this lecture, he focuses on Liouville's Theorem, which he describes as one of the basis for Hamiltonian mechanics. He works to prove the reversibility of classical mechanics. This course is the beginning of a six course sequence that explores the theoretical foundations of modern physics. Topics in the series include classical mechanics, quantum mechanics, theories of relativity, electromagnetism, cosmology, and black holes. Stanford University http://www.stanford.edu/ Stanford Continuing Studies http:/continuingstudies.stanford.edu/ Stanford University Channel on YouTube: http://www.youtube.com/stanford
Jacob Linder: 26.01.2012, Classical Mechanics (TFY4345), V2012 NTNU A full textbook covering the material in the lectures in detail can be downloaded for free here: http://bookboon.com/en/introduction-to-lagrangian-hamiltonian-mechanics-ebook
Alvaro Pelayo Member, School of Mathematics April 4, 2011 I will start with a review the basic notions of Hamiltonian/symplectic vector field and of Hamiltonian/symplectic group action, and the classical structure theorems of Kostant, Atiyah, Guillemin-Sternberg and Delzant on Hamiltonian torus actions. Then I will state a structure theorem for general symplectic torus actions, and give an idea of its proof. In the second part of the talk I will introduce new symplectic invariants of completely integrable Hamiltonian systems in low dimensions, and explain how these invariants determine, up to isomorphisms, the so called "semitoric systems". Semitoric systems are Hamiltonian systems which lie somewhere between the more rigid toric systems and the usually complicated general integrable syste...
Derivation of the Hamilton equations of motion and the Hamiltonian.
Princeton/IAS Symplectic Geometry Seminar Topic:C0C0 Hamiltonian dynamics and a counterexample to the Arnold conjecture Speaker: Sobhan Seyfaddini Affiliation: Member, School of Mathematics Date: November 29, 2016 For more videos, visit http://video.ias.edu
Daniel Sutton: An effective description of Hamiltonian dynamics via the Maupertuis principle We study effective descriptions for the motion of a particle moving in a bounded periodic potential, as governed by Newton's second law. In particular we seek an effective equation, describing the motion of the particle in a rapidly oscillating potential. The study of such problems was initiated by P. L. Lions, G. Papanicolaou and S. R. S. Varadhan (1987) through the homogenisation of the Hamilton-Jacobi PDE. We propose an alternative approach, that is to use the principle of Maupertuis (1744). In this alternative formulation, which characterises dynamical trajectories as geodesics in a Riemannian manifold, we are able to describe properties of effective Hamiltonians in certain cases; specifically...
MIT 2.003SC Engineering Dynamics, Fall 2011 View the complete course: http://ocw.mit.edu/2-003SCF11 Instructor: J. Kim Vandiver License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
Optimal Control by Prof. G.D. Ray,Department of Electrical Engineering,IIT Kharagpur.For more details on NPTEL visit http://nptel.ac.in
Jacob Linder: 12.04.2012, Classical Mechanics (TFY4345), v2012 NTNU A full textbook covering the material in the lectures in detail can be downloaded for free here: http://bookboon.com/en/introduction-to-lagrangian-hamiltonian-mechanics-ebook
Join Jeff Poppen, 'the Barefoot Farmer' for day one of this two day biodynamics intensive based on the teachings of Rudolf Steiner. Amy Hamilton and Craig Ciska also share their experience and wisdom in this workshop. Biodynamics includes subtle yet powerful methods that work with the synergy and dynamics of nature to cultivate more dynamically alive soils and nutrient rich harvests.
Lecture series on Dynamics of Physical System by Prof. Soumitro Banerjee, Department of Electrical Engineering, IIT Kharagpur.For more details on NPTEL visit http://nptel.iitm.ac.in
Lecture Series on Classical Physics by Prof.V.Balakrishnan, Department of Physics, IIT Madras. For more details on NPTEL visit http://nptel.iitm.ac.in
Part 6 of a series: setting out the Energy operator, the Hamiltonian and deriving Schrodinger's Equation.
In this lecture you will learn: Introduction to Hamiltonian dynamics. Made by: Department of Physics, IIT Madras. This video is part of the playlist "University Lectures". For further interesting topics you can look here: https://www.youtube.com/playlist?list=PLdId9dvaMGZPorXrqBHGYn788r1vjVkXl "Hamiltonian mechanics is a theory developed as a reformulation of classical mechanics and predicts the same outcomes as non-Hamiltonian classical mechanics." https://en.wikipedia.org/wiki/Hamiltonian_mechanics This video was made by another YouTube user and made available for the use under the Creative Commons licence "CC-BY". Source channel: https://www.youtube.com/user/nptelhrd