Euler's equations of motion

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A set of three differential equations expressing relations between the force moments, angular velocities, and angular accelerations of a rotating rigid body. They are equations of motion in the usual dynamical sense, of forms (1)–(3).

(1)

(2)

(3)

The formulation employs as coordinate axes the three principal axes of rotational inertia of the body that can rotate about a body-fixed point, which is the center of mass if constraints are absent. These reference axes, which form a righthand set, are indicated by subscripts 1, 2, and 3 in the equations, where I₁, I₂, and I₃ represent the principal moments of inertia; ω₁, ω₂, and ω₃ the angular velocities about the axes; M₁, M₂, and M₃ the corresponding force moments; and t the time. See Rigid-body dynamics

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No references found			This was chiefly because, starting from Euler's equations of motion, the science had become more and more a purely academic analysis of the hypothetical frictionless "ideal fluid. Economics as an inductive science by Clower, Robert W. / Southern Economic Journal			Eulamellibranchia Eulenburg's disease Eulenburg, Philipp, Fürst zu Eulenspiegel, Till Euler Euler Angles Euler Characteristic Euler characteristic of a topological space X Euler diagram Euler equation Euler equations of motion Euler force Euler formula for long columns Euler method Euler Number Euler number 1 Euler number 2 Euler Numbers Euler Phi-Function Euler Substitutions Euler transformation Euler's Constant Euler's criterion Euler's Equation Euler's Equations Euler's equations of motion Euler's expansion Euler's Formula Euler's Integral Euler's numbers Euler's phi function Euler's spiral Euler's theorem Euler, Leonhard Euler, Ulf Svante Von Euler-Chelpin Euler-Chelpin, Hans Karl August Simon Von Euler-Fourier Formulas Euler-Lagrange equation Euler-Maclaurin formula Euler-Maclaurin Summation Formula Euler-Rodrigues parameter Eulerian coordinates Eulerian correlation Eulerian description Eulerian equation Eulerian graph Eulerian nutation Eulerian path Eulerian wind Euless			Euler polyhedron theorem Euler quadratic residue theorem Euler rotation Euler Substitutions Euler summation formula Euler theorem Euler theorem on homogeneous functions Euler totient rule Euler totient theorem Euler tour Euler trail Euler transformation Euler Venn diagram Euler walk Euler wenn diagram Euler zeta function Euler's angle Euler's Box Euler's Box Euler's circles Euler's constant Euler's criterion Euler's equation Euler's equation of motion Euler's equations Euler's equations of motion Euler's expansion Euler's formula Euler's formula for polyhedra Euler's formula in complex analysis Euler's forward method Euler's generalization Euler's homogeneous function theorem Euler's Integral Euler's method Euler's numbers Euler's phi function Euler's polyhedron formula Euler's polyhedron theorem Euler's quadratic residue theorem Euler's spiral Euler's summation formula Euler's theorem Euler's theorem on homogeneous functions Euler's totient function Euler's totient rule Euler's totient theorem Euler, Leonhard Euler, Leonhard Euler, Leonhard Euler, Ulf Svante von Euler, Ulf Svante von Euler, Ulf Svante von Euler-Chelpin Euler-Chelpin

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