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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. They are named in honour of Leonhard Euler. Their general vector form is
The cam can be seen as a device that converts rotational motion to reciprocating (or sometimes oscillating) motion. [clarification needed] [3] A common example is the camshaft of an automobile, which takes the rotary motion of the engine and converts it into the reciprocating motion necessary to operate the intake and exhaust valves of the cylinders.
In classical mechanics, the Euler acceleration (named for Leonhard Euler), also known as azimuthal acceleration [8] or transverse acceleration [9] is an acceleration that appears when a non-uniformly rotating reference frame is used for analysis of motion and there is variation in the angular velocity of the reference frame's axis. This article ...
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.
The moment of inertia plays the role in rotational kinetics that mass (inertia) plays in linear kinetics—both characterize the resistance of a body to changes in its motion. The moment of inertia depends on how mass is distributed around an axis of rotation, and will vary depending on the chosen axis.
In motion control, the design focus is on straight, linear motion, with the need to move a system from one steady position to another (point-to-point motion). The design concern from a jerk perspective is vertical jerk; the jerk from tangential acceleration is effectively zero since linear motion is non-rotational.
a cm is the linear acceleration of the center of mass of the body, m is the mass of the body, α is the angular acceleration of the body, and; I is the moment of inertia of the body about its center of mass. See also Euler's equations (rigid body dynamics).
The solution of these equations of motion provides a description of the position, the motion and the acceleration of the individual components of the system, and overall the system itself, as a function of time. The formulation and solution of rigid body dynamics is an important tool in the computer simulation of mechanical systems.