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Newton's laws are often stated in terms of point or particle masses, that is, bodies whose volume is negligible. This is a reasonable approximation for real bodies when the motion of internal parts can be neglected, and when the separation between bodies is much larger than the size of each.
Once independent relations for each force acting on a particle are available, they can be substituted into Newton's second law to obtain an ordinary differential equation, which is called the equation of motion. As an example, assume that friction is the only force acting on the particle, and that it may be modeled as a function of the velocity ...
A theory of everything (TOE), final theory, ultimate theory, unified field theory, or master theory is a singular, all-encompassing, coherent theoretical framework of physics that fully explains and links together all aspects of the universe. [1]: 6 Finding a theory of everything is one of the major unsolved problems in physics. [2] [3]
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.
Even at relativistic speeds four-acceleration is related to the four-force: =, where m is the invariant mass of a particle. When the four-force is zero, only gravitation affects the trajectory of a particle, and the four-vector equivalent of Newton's second law above reduces to the geodesic equation. The four-acceleration of a particle ...
In Cartesian coordinates the Lagrangian of a non-relativistic classical particle in an electromagnetic field is (in SI Units): = ˙ + ˙, where q is the electric charge of the particle, φ is the electric scalar potential, and the A i are the components of the magnetic vector potential that may all explicitly depend on and .
In the simple case of a single particle moving with a constant velocity (thereby undergoing uniform linear motion), the action is the momentum of the particle times the distance it moves, added up along its path; equivalently, action is the difference between the particle's kinetic energy and its potential energy, times the duration for which ...
For example, when rotating a stationary (zero momentum) spin-5 particle about its center, is a rotation in 3D space (an element of ()), while () is an operator whose domain and range are each the space of possible quantum states of this particle, in this example the projective space associated with an 11-dimensional complex Hilbert space .