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
Linear elasticity fourth-order stiffness tensor, formula_8 is the body force per unit volume, formula_9 is the mass density, formula_10 represents the nabla operator, formula_11 represents a transpose, formula_12 represents the second derivative with respect to time, and formula_13 is the inner product of two second-order tensors (summation over repeated indices is implied). Expressed in terms of components with respect to a rectangular Cartesian coordinate system, the governing equations of linear elasticity are: An elastostatic boundary value problem for an isotropic-homogeneous media is a system of 15 independent equations and equal number of unknowns (3 equilibrium equations, 6 strain-displacement equations, and 6 constitutive