Euler's laws of motion 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, (also denoted ) is equal to the product of the mass of the body and the velocity of its center of mass : Internal forces between the particles that make up a body do not contribute to changing the total momentum of the body as there
Angular velocity of bases. For example, changing to the mobile frame: where formula_46 are unit vectors for the frame fixed in the moving body. This example has been made using the Z-X-Z convention for Euler angles. The angular velocity vector formula_47 defined above may be equivalently expressed as an angular velocity tensor, the matrix (or linear mapping) "W" = "W"("t") defined by: This is an infinitesimal rotation matrix. The linear mapping "W" acts as formula_49: A vector formula_51 undergoing uniform circular motion around an axis satisfies: Given the orientation matrix "A"("t") of a frame, whose columns are the moving orthonormal coordinate vectors