terms of generalized coordinates. In the formulation of virtual work, each generalized force is the coefficient of the variation of a generalized coordinate...

reference state. The generalized velocities are the time derivatives of the generalized coordinates of the system. The adjective "generalized" distinguishes...

{q}}}}\right),} is the generalized force acting on this one degree of freedom system. If the mechanical system is defined by m generalized coordinates, qj,...

system, known as Lagrange's equations or the generalized equations of motion. If the generalized forces Qj are derivable from a potential energy V(q1...

Given this vk, the kinetic energy in generalized coordinates depends on the generalized velocities, generalized coordinates, and time if the position...

(condensation). Only when these "forces" equilibrate is equilibrium obtained. Generalized coordinate and generalized force: analogous conjugate variable...

{\theta }}^{2}.} The generalized coordinates of the system are θ {\displaystyle \theta } and x {\displaystyle x} , each has a generalized force. On the x {\displaystyle...

the forces of constraint vanish. That is to say that the generalized forces Q j {\displaystyle \mathbf {Q} _{j}} need not include constraint forces. It...

Retrieved 2020-11-09. For a description of generalized coordinates, see Ahmed A. Shabana (2003). "Generalized coordinates and kinematic constraints". Dynamics...

in the context as generalized coordinates. The kinetic and potential energies of the system are expressed using these generalized coordinates or momenta...

_{i}\,\mathrm {d} n_{i}\,} Here the X j {\displaystyle X_{j}} are the generalized forces corresponding to the external parameters x j {\displaystyle x_{j}}...

the Lagrangian which is a function of the generalized coordinates and the associated velocities. If all forces are derivable from a potential, then the...

external variables, and the X i {\displaystyle X_{i}} the corresponding generalized forces. A system kept at constant volume, temperature, and particle number...

Frenet–Serret formulas Galilean invariance General relativity Generalized coordinates Generalized forces Geodetic reference frame Inertial frame of reference Local...

the temperature is known as a "generalized" force (rather than an actual mechanical force) and the entropy is a generalized displacement. Similarly, a difference...

is reduced to a minimum. The time derivatives of the generalized coordinates are the generalized velocities q ˙ = d q d t . {\displaystyle \mathbf {\dot...

in the internal coordinates, so it can also be written in terms of generalized forces. The resulting coefficients are termed compliance constants. A direct...

primes today are generalized Fermat primes. Generalized Fermat numbers can be prime only for even a, because if a is odd then every generalized Fermat number...

_{r}={\ddot {q}}_{r}} is an arbitrary generalized acceleration, or the second time derivative of the generalized coordinates q r {\displaystyle q_{r}}...

conserved quantity is generalized momentum, and in general this is different from the kinetic momentum defined above. The concept of generalized momentum is carried...

published his Traité de dynamique, in which he introduced the concept of generalized forces for accelerating systems and systems with constraints, and applied...

publishes his Traite de Dynamique, in which he introduces the concept of generalized forces and D'Alembert's principle 1747 – D'Alembert and Alexis Clairaut publish...

motion equation Frenet–Serret formulas General relativity Generalized coordinates Generalized force Gravity Inertial reference frame Kinematics Kinetics...

{d} N_{j}+\sum _{i}X_{i}\,\mathrm {d} x_{i}} Here the Xi are the generalized forces corresponding to the external variables xi. Applying Legendre transforms...

modern armed forces undergo generalized basic CBRN self-defense training for all their personnel. Central Laboratory of the Armed Forces – Military Unit...

Moldova and Ukraine did not sign the documents on the creation of generalized CIS Joint Forces and did not agree with the principle despite membership in the...

system, if all forces, with the exception of the constraint forces, are derivable from the generalized scalar potential, and this generalized scalar potential...

specific to their own occupational specialty, as opposed to the more generalized command responsibilities of commissioned officers.[excessive citations]...

Einstein tried to form a generalized theory of gravitation that would unify the gravitational and electromagnetic forces (and perhaps others), guided...

currents I {\displaystyle I} and current-induced forces F {\displaystyle F} , taken as generalized fluxes on one hand, and the chemical potentials biases...