Euler's formula (English: Euler's formula, also known as Euler's formula) is a formula in the field of complex analysis, which links trigonometric functions with complex exponential functions and is named after its inventor leonhard euler. Euler's formula suggests that for any real number? {\displaystyle x}, both exist.

Euler equation, that is, differential equation of motion, belongs to the most important basic equation in inviscid fluid dynamics, and refers to the differential equation of motion obtained by applying Newton's second law to inviscid fluid micelles. Euler equation is widely used. 1755, the Swiss mathematician L. Euler first proposed this equation in his book General Principles of Fluid Motion.

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In physics, Euler equation dominates the rotation of rigid body. We can choose the principal axis coordinate relative to inertia as the body coordinate system. This simplifies the calculation, because we can now divide the change of angular momentum into two parts: the size change and the direction change, and further diagonalize the inertia.

In fluid dynamics, Euler equation is a set of equations that control the motion of inviscid fluid, named after leonhard euler. Each equation of the system represents the conservation of mass (continuity), momentum and energy respectively, and corresponds to the Navier-Stokes equation with zero viscosity and no heat conduction term. In history, only continuity and momentum equations were derived by Euler. However, the whole set of equations including energy equation is often called "Euler equation" in the literature of fluid dynamics.

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