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Since the magnetic Lorentz force is always perpendicular to the magnetic field, it has no influence (to lowest order) on the parallel motion. In a uniform field with no additional forces, a charged particle will gyrate around the magnetic field according to the perpendicular component of its velocity and drift parallel to the field according to its initial parallel velocity, resulting in a ...
The rigid body's motion is entirely determined by the motion of its inertia ellipsoid, which is rigidly fixed to the rigid body like a coordinate frame. Its inertia ellipsoid rolls, without slipping, on the invariable plane , with the center of the ellipsoid a constant height above the plane.
The above formula means that the component of the curl of a vector field along a certain axis is the infinitesimal area density of the circulation of the field in a plane perpendicular to that axis. This formula does not a priori define a legitimate vector field, for the individual circulation densities with respect to various axes a priori ...
In Cartesian coordinates, the divergence of a continuously differentiable vector field = + + is the scalar-valued function: = = (, , ) (, , ) = + +.. As the name implies, the divergence is a (local) measure of the degree to which vectors in the field diverge.
The equation of motion of a fluid on a streamline for a flow in a vertical plane is ... is related to the pressure gradient acting perpendicular to the streamline ...
The gradient theorem states that if the vector field F is the gradient of some scalar-valued function (i.e., if F is conservative), then F is a path-independent vector field (i.e., the integral of F over some piecewise-differentiable curve is dependent only on end points). This theorem has a powerful converse:
The solution to this equation when there is no applied torque is discussed in the articles Euler's equation of motion and Poinsot's ellipsoid. It follows from Euler's equation that a torque τ applied perpendicular to the axis of rotation, and therefore perpendicular to L, results in a rotation about an axis perpendicular to both τ and L.
In classical mechanics, the central-force problem is to determine the motion of a particle in a single central potential field.A central force is a force (possibly negative) that points from the particle directly towards a fixed point in space, the center, and whose magnitude only depends on the distance of the object to the center.