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In classical mechanics, Euler's rotation equations are a vectorial quasilinear first-order ordinary differential equation describing the rotation of a rigid body, using a rotating reference frame with angular velocity ω whose axes are fixed to the body.
Kinematics is often described as applied geometry, where the movement of a mechanical system is described using the rigid transformations of Euclidean geometry. The coordinates of points in a plane are two-dimensional vectors in R 2 (two dimensional space).
There are two main descriptions of motion: dynamics and kinematics.Dynamics is general, since the momenta, forces and energy of the particles are taken into account. In this instance, sometimes the term dynamics refers to the differential equations that the system satisfies (e.g., Newton's second law or Euler–Lagrange equations), and sometimes to the solutions to those equations.
Screw theory is the algebraic calculation of pairs of vectors, also known as dual vectors [1] – such as angular and linear velocity, or forces and moments – that arise in the kinematics and dynamics of rigid bodies.
In the physical science of dynamics, rigid-body dynamics studies the movement of systems of interconnected bodies under the action of external forces.The assumption that the bodies are rigid (i.e. they do not deform under the action of applied forces) simplifies analysis, by reducing the parameters that describe the configuration of the system to the translation and rotation of reference ...
Studies of two-dimensional collisions are conducted for many bodies in the framework of a two-dimensional gas. Two-dimensional elastic collision. In a center of momentum frame at any time the velocities of the two bodies are in opposite directions, with magnitudes inversely proportional to the masses. In an elastic collision these magnitudes do ...
In classical mechanics, a kinematic pair is a connection between two physical objects that imposes constraints on their relative movement ().German engineer Franz Reuleaux introduced the kinematic pair as a new approach to the study of machines [1] that provided an advance over the notion of elements consisting of simple machines.
where b is the force acting on the body per unit mass (dimensions of acceleration, misleadingly called the "body force"), and dm = ρ dV is an infinitesimal mass element of the body. Body forces and contact forces acting on the body lead to corresponding moments ( torques ) of those forces relative to a given point.