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- Jacobi_coordinates abstract "In the theory of many-particle systems, Jacobi coordinates often are used to simplify the mathematical formulation. These coordinates are particularly common in treating polyatomic molecules and chemical reactions, and in celestial mechanics. An algorithm for generating the Jacobi coordinates for N bodies may be based upon binary trees. In words, the algorithm is described as follows:Let mj and mk be the masses of two bodies that are replaced by a new body of virtual mass M = mj + mk. The position coordinates xj and xk are replaced by their relative position rjk = xj − xk and by the vector to their center of mass Rjk = (mj qj + mkqk)/(mj + mk). The node in the binary tree corresponding to the virtual body has mj as its right child and mk as its left child. The order of children indicates the relative coordinate points from xk to xj. Repeat the above step for N − 1 bodies, that is, the N − 2 original bodies plus the new virtual body. For the four-body problem the result is:withThe vector R is the center of mass of all the bodies: The result one is left with is thus a system of N translationally-invariant coordinates and a reduced mass, from iteratively treats and reducing two-body systems within the many-body system.".
- Jacobi_coordinates thumbnail Two-body_Jacobi_coordinates.JPG?width=300.
- Jacobi_coordinates wikiPageID "23098762".
- Jacobi_coordinates wikiPageRevisionID "596465631".
- Jacobi_coordinates hasPhotoCollection Jacobi_coordinates.
- Jacobi_coordinates subject Category:Chemical_reactions.
- Jacobi_coordinates subject Category:Coordinate_systems.
- Jacobi_coordinates subject Category:Hamiltonian_mechanics.
- Jacobi_coordinates subject Category:Lagrangian_mechanics.
- Jacobi_coordinates subject Category:Molecular_geometry.
- Jacobi_coordinates subject Category:Molecular_vibration.
- Jacobi_coordinates subject Category:Orbits.
- Jacobi_coordinates type Abstraction100002137.
- Jacobi_coordinates type Arrangement105726596.
- Jacobi_coordinates type Cognition100023271.
- Jacobi_coordinates type CoordinateSystem105728024.
- Jacobi_coordinates type CoordinateSystems.
- Jacobi_coordinates type PsychologicalFeature100023100.
- Jacobi_coordinates type Structure105726345.
- Jacobi_coordinates comment "In the theory of many-particle systems, Jacobi coordinates often are used to simplify the mathematical formulation. These coordinates are particularly common in treating polyatomic molecules and chemical reactions, and in celestial mechanics. An algorithm for generating the Jacobi coordinates for N bodies may be based upon binary trees. In words, the algorithm is described as follows:Let mj and mk be the masses of two bodies that are replaced by a new body of virtual mass M = mj + mk.".
- Jacobi_coordinates label "Coordenadas de Jacobi".
- Jacobi_coordinates label "Jacobi coordinates".
- Jacobi_coordinates label "雅可比坐標".
- Jacobi_coordinates sameAs Coordenadas_de_Jacobi.
- Jacobi_coordinates sameAs m.0jt1c4m.
- Jacobi_coordinates sameAs Q5409661.
- Jacobi_coordinates sameAs Q5409661.
- Jacobi_coordinates sameAs Jacobi_coordinates.
- Jacobi_coordinates wasDerivedFrom Jacobi_coordinates?oldid=596465631.
- Jacobi_coordinates depiction Two-body_Jacobi_coordinates.JPG.
- Jacobi_coordinates isPrimaryTopicOf Jacobi_coordinates.