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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 dynamics of an interconnected system of rigid bodies, Bi, j = 1, ..., M, is formulated by isolating each rigid body and introducing the interaction forces. The resultant of the external and interaction forces on each body, yields the force-torque equations. Newton's formulation yields 6 M equations that define the dynamics of a system of M ...
In classical mechanics, the Newton–Euler equations describe the combined translational and rotational dynamics of a rigid body. [1][2] [3][4][5] Traditionally the Newton–Euler equations is the grouping together of Euler's two laws of motion for a rigid body into a single equation with 6 components, using column vectors and matrices.
v. t. e. Rotation around a fixed axis or axial rotation is a special case of rotational motion around an axis of rotation fixed, stationary, or static in three-dimensional space. This type of motion excludes the possibility of the instantaneous axis of rotation changing its orientation and cannot describe such phenomena as wobbling or precession.
The Euler angles are three angles introduced by Swiss mathematician Leonhard Euler (1707–1783) to describe the orientation of a rigid body with respect to a fixed coordinate system. [1] Left: A gimbal set, showing a z - x - z rotation sequence. External frame shown in the base. Internal axes in red color.
Torque-induced precession (gyroscopic precession) is the phenomenon in which the axis of a spinning object (e.g., a gyroscope) describes a cone in space when an external torque is applied to it. The phenomenon is commonly seen in a spinning toy top, but all rotating objects can undergo precession. If the speed of the rotation and the magnitude ...
In mathematics, a rotating body is commonly represented by a pseudovector along the axis of rotation. The length of the vector gives the speed of rotation and the direction of the axis gives the direction of rotation according to the right-hand rule: right fingers curled in the direction of rotation and the right thumb pointing in the positive ...
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. [2][3] Screw theory provides a mathematical formulation for the geometry of lines which is central to rigid body dynamics ...