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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.
Phasor notation (also known as angle notation) is a mathematical notation used in electronics engineering and electrical engineering.A vector whose polar coordinates are magnitude and angle is written . [13] can represent either the vector (, ) or the complex number + =, according to Euler's formula with =, both of which have magnitudes of 1.
Euler's second law states that the rate of change of angular momentum L about a point that is fixed in an inertial reference frame (often the center of mass of the body), is equal to the sum of the external moments of force acting on that body M about that point: [1] [4] [5]
One may instead change to a coordinate frame fixed in the rotating body, in which the moment of inertia tensor is constant. Using a reference frame such as that at the center of mass, the frame's position drops out of the equations. In any rotating reference frame, the time derivative must be replaced so that the equation becomes
The motion of a body in which it moves to and from a definite point is also called oscillatory motion or vibratory motion. The time period is able to be calculated by T = 2 π l g {\displaystyle T=2\pi {\sqrt {\frac {l}{g}}}} where l is the distance from rotation to the object's center of mass undergoing SHM and g is gravitational acceleration.
the mass–energy equivalence formula which gives the energy in terms of the momentum and the rest mass of a particle. The equation for the mass shell is also often written in terms of the four-momentum ; in Einstein notation with metric signature (+,−,−,−) and units where the speed of light c = 1 {\displaystyle c=1} , as p μ p μ ≡ p ...
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. These laws relate the motion of the center of gravity of a rigid body with the sum of forces and torques (or synonymously moments) acting on the rigid body.
The equation of motion for a particle of constant mass m is Newton's second law of 1687, in modern vector notation =, where a is its acceleration and F the resultant force acting on it. Where the mass is varying, the equation needs to be generalised to take the time derivative of the momentum.