Mécanique analytique¶
Lagrange, J. (1815). Mécanique analytique.
Cited by¶
7 citations across 7 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Constraint
- (4) The deeper abstraction is that **constraint reasoning is the structural prerequisite for all disciplined decision-making under restriction: Lagrange's 1788 Mécanique Analytique
This sourceMultiplier technique originates in Lagrange's 1760s–70s calculus-of-variations memoirs. Historical treatment: Fraser, "Lagrange's Analytical Mathematics, Its Cartesian Origins and Reception in Comte's Positive Philosophy." Studies in History and Philosophy of Science 21, no. 2 (1990): 243–256; Goldstine, A History of the Calculus of Variations from the 17th through the 19th Century (Springer, 1980).
- (4) The deeper abstraction is that **constraint reasoning is the structural prerequisite for all disciplined decision-making under restriction: Lagrange's 1788 Mécanique Analytique
- Degrees of Freedom
- The construct originates in Lagrange's generalized-coordinate framework
This sourceHistorical treatment: Fraser, "Lagrange's Analytical Mathematics, Its Cartesian Origins and Reception in Comte's Positive Philosophy"90024-3). Studies in History and Philosophy of Science 21, no. 2 (1990): 243–256; Goldstine, A History of the Calculus of Variations from the 17th through the 19th Century (Springer, 1980).
- The construct originates in Lagrange's generalized-coordinate framework
- Duality
- … cross-side inference: once the pairing is explicit and the preserved structure is named, theorems proved on one side immediately imply dual theorems on the other (doubling the payoff of each result), optimization problems that are hard in primal form can be recast and solved in dual form (where the Lagrangian dual
This sourceMultiplier technique originates in Lagrange's 1760s–70s calculus-of-variations memoirs. Historical treatment: Fraser, "Lagrange's Analytical Mathematics, Its Cartesian Origins and Reception in Comte's Positive Philosophy." Studies in History and Philosophy of Science 21, no. 2 (1990): 243–256; Goldstine, A History of the Calculus of Variations from the 17th through the 19th Century (Springer, 1980).
- … cross-side inference: once the pairing is explicit and the preserved structure is named, theorems proved on one side immediately imply dual theorems on the other (doubling the payoff of each result), optimization problems that are hard in primal form can be recast and solved in dual form (where the Lagrangian dual
- Noether's Theorem
- The variational structure underlying Noether's theorem roots in Lagrange (1788)
This sourceMultiplier technique originates in Lagrange's 1760s–70s calculus-of-variations memoirs. Historical treatment: Fraser, "Lagrange's Analytical Mathematics, Its Cartesian Origins and Reception in Comte's Positive Philosophy." Studies in History and Philosophy of Science 21, no. 2 (1990): 243–256; Goldstine, A History of the Calculus of Variations from the 17th through the 19th Century (Springer, 1980).
- The variational structure underlying Noether's theorem roots in Lagrange (1788)
- Oscillation
- Lagrange's 1788 Mécanique analytique
This sourceMultiplier technique originates in Lagrange's 1760s–70s calculus-of-variations memoirs. Historical treatment: Fraser, "Lagrange's Analytical Mathematics, Its Cartesian Origins and Reception in Comte's Positive Philosophy." Studies in History and Philosophy of Science 21, no. 2 (1990): 243–256; Goldstine, A History of the Calculus of Variations from the 17th through the 19th Century (Springer, 1980).
- Lagrange's 1788 Mécanique analytique
- Perturbation
- Reference state. A baseline — equilibrium configuration, exact solvable limit, well-understood operating point, current trajectory — is specified. Small departure. The perturbation is small in a specifiable sense (amplitude as fraction of baseline, energy as fraction of characteristic energy, probability as distance from typical realization). Linearized or expanded response. System response is analyzed as a series expansion in the perturbation amplitude — linear term, quadratic correction, higher orders — or as an ensemble of small-perturbation responses.
This sourceMultiplier technique originates in Lagrange's 1760s–70s calculus-of-variations memoirs. Historical treatment: Fraser, "Lagrange's Analytical Mathematics, Its Cartesian Origins and Reception in Comte's Positive Philosophy." Studies in History and Philosophy of Science 21, no. 2 (1990): 243–256; Goldstine, A History of the Calculus of Variations from the 17th through the 19th Century (Springer, 1980).
- Reference state. A baseline — equilibrium configuration, exact solvable limit, well-understood operating point, current trajectory — is specified. Small departure. The perturbation is small in a specifiable sense (amplitude as fraction of baseline, energy as fraction of characteristic energy, probability as distance from typical realization). Linearized or expanded response. System response is analyzed as a series expansion in the perturbation amplitude — linear term, quadratic correction, higher orders — or as an ensemble of small-perturbation responses.
- Principle of Least Action
- The principle of least action (more precisely, the principle of stationary action) is the foundational variational principle of classical and quantum physics, which states that the actual trajectory of a physical system between specified initial and final configurations is the one that makes a particular integral functional — the action S = ∫L dt (where L is the Lagrangian, the difference between kinetic and potential energy in the simplest case) — stationary with respect to small variations of the trajectory.
This sourceMultiplier technique originates in Lagrange's 1760s–70s calculus-of-variations memoirs. Historical treatment: Fraser, "Lagrange's Analytical Mathematics, Its Cartesian Origins and Reception in Comte's Positive Philosophy." Studies in History and Philosophy of Science 21, no. 2 (1990): 243–256; Goldstine, A History of the Calculus of Variations from the 17th through the 19th Century (Springer, 1980).
- The principle of least action (more precisely, the principle of stationary action) is the foundational variational principle of classical and quantum physics, which states that the actual trajectory of a physical system between specified initial and final configurations is the one that makes a particular integral functional — the action S = ∫L dt (where L is the Lagrangian, the difference between kinetic and potential energy in the simplest case) — stationary with respect to small variations of the trajectory.
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