Euler's laws of motion

In classical mechanics, Euler's laws of motion are equations of motion which extend Newton's laws of motion for point particle to rigid body motion. They were formulated by Leonhard Euler about 50 years after Isaac Newton formulated his laws.

Euler's first law states that the linear momentum of a body, $p$ (also denoted $G$ ) is equal to the product of the mass of the body $m$ and the velocity of its center of mass $v cm$ :

Internal forces between the particles that make up a body do not contribute to changing the total momentum of the body as there is an equal and opposite force resulting in no net effect. The law is also stated as:

where $a cm = d v cm / dt$ is the acceleration of the centre of mass and $F = d p / dt$ is the total applied force on the body. This is just the time derivative of the previous equation ( $m$ is a constant).

Euler's second law states that the rate of change of angular momentum $L$ (sometimes denoted $H$ ) about a point that is fixed in an inertial reference frame (often the mass center of the body), is equal to the sum of the external moments of force (torques) acting on that body $M$ (also denoted $τ$ or $Γ$ ) about that point:

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