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Kinetic energy of a multibody system. This function returns the kinetic energy of a system of Particle's and/or RigidBody's. The kinetic energy of such a system is equal to the sum of the kinetic energies of its constituents. Consider a system, S, comprising a rigid body, A, and a particle, P. The kinetic energy of the system, T, is equal to the vector sum of the kinetic energy of the particle, T1, and the kinetic energy of the rigid body, T2, i.e. T = T1 + T2(more...)

def kinetic_energy(frame, *body): """Kinetic energy of a multibody system. This function returns the kinetic energy of a system of Particle's and/or RigidBody's. The kinetic energy of such a system is equal to the sum of the kinetic energies of its constituents. Consider a system, S, comprising a rigid body, A, and a particle, P. The kinetic energy of the system, T, is equal to the vector sum of the kinetic energy of the particle, T1, and the kinetic energy of the rigid body, T2, i.e. T = T1 + T2 Kinetic energy is a scalar. Parameters ========== frame : ReferenceFrame The frame in which the velocity or angular velocity of the body is defined. body1, body2, body3... : Particle and/or RigidBody The body (or bodies) whose kinetic energy is required. Examples ======== >>> from sympy.physics.mechanics import Point, Particle, ReferenceFrame >>> from sympy.physics.mechanics import RigidBody, outer, kinetic_energy >>> N = ReferenceFrame('N') >>> O = Point('O') >>> O.set_vel(N, 0 * N.x) >>> P = O.locatenew('P', 1 * N.x) >>> P.set_vel(N, 10 * N.x) >>> Pa = Particle('Pa', P, 1) >>> Ac = O.locatenew('Ac', 2 * N.y) >>> Ac.set_vel(N, 5 * N.y) >>> a = ReferenceFrame('a') >>> a.set_ang_vel(N, 10 * N.z) >>> I = outer(N.z, N.z) >>> A = RigidBody('A', Ac, a, 20, (I, Ac)) >>> kinetic_energy(N, Pa, A) 350 """ if not isinstance(frame, ReferenceFrame): raise TypeError('Please enter a valid ReferenceFrame') ke_sys = S(0) for e in body: if isinstance(e, (RigidBody, Particle)): ke_sys += e.kinetic_energy(frame) else: raise TypeError('*body must have only Particle or RigidBody') return ke_sys

**sympy**(Download)

from sympy import symbols, sin, cos, sqrt, pi from sympy.physics.mechanics import (cross, dot, dynamicsymbols, express, ReferenceFrame, inertia, Point, kinematic_equations, Vector, inertia_of_point_mass, partial_velocity,

I = outer(N.z, N.z) A = RigidBody('A', Ac, a, M, (I, Ac)) assert 0 == kinetic_energy(N, Pa, A) - (M*l1**2*omega**2/2 + 2*l1**2*m*omega**2 + omega**2/2)

src/s/y/sympy-HEAD/sympy/physics/mechanics/tests/test_lagrange.py

**sympy**(Download)

from sympy.physics.mechanics import (dynamicsymbols, ReferenceFrame, Point, RigidBody, LagrangesMethod, Particle, kinetic_energy, dynamicsymbols, inertia, potential_energy, Lagrangian) from sympy import symbols, pi, sin, cos, tan, simplify, expand, Function, \