def _form_fr(self, fl): """Form the generalized active force.""" if not iterable(fl): raise TypeError('Force pairs must be supplied in an iterable.') N = self._inertial # pull out relevant velocities for constructing partial velocities vel_list, f_list = _f_list_parser(fl, N) vel_list = [i.subs(self._qdot_u_map) for i in vel_list] # Fill Fr with dot product of partial velocities and forces o = len(self._u) b = len(f_list) FR = zeros(o, 1) partials = partial_velocity(vel_list, self._u, N) for i in range(o): FR[i] = sum(partials[j][i] & f_list[j] for j in range(b)) # In case there are dependent speeds if self._udep: p = o - len(self._udep) FRtilde = FR[:p, 0] FRold = FR[p:o, 0] FRtilde += self._Ars.T * FRold FR = FRtilde self._fr = FR return FR
def _form_fr(self, fl): """Form the generalized active force.""" if fl != None and (len(fl) == 0 or not iterable(fl)): raise ValueError('Force pairs must be supplied in an ' 'non-empty iterable or None.') N = self._inertial # pull out relevant velocities for constructing partial velocities vel_list, f_list = _f_list_parser(fl, N) vel_list = [msubs(i, self._qdot_u_map) for i in vel_list] # Fill Fr with dot product of partial velocities and forces o = len(self.u) b = len(f_list) FR = zeros(o, 1) partials = partial_velocity(vel_list, self.u, N) for i in range(o): FR[i] = sum(partials[j][i] & f_list[j] for j in range(b)) # In case there are dependent speeds if self._udep: p = o - len(self._udep) FRtilde = FR[:p, 0] FRold = FR[p:o, 0] FRtilde += self._Ars.T * FRold FR = FRtilde self._forcelist = fl self._fr = FR return FR
def _partial_velocity(self, vlist, ulist, frame): """Returns the list of partial velocities, replacing qdot's in the velocity list if necessary. """ if self._qdot_u_map is None: raise ___KDEqError v = [vel.subs(self._qdot_u_map) for vel in vlist] return partial_velocity(v, ulist, frame)
def get_partial_velocity(body): if isinstance(body, RigidBody): vlist = [body.masscenter.vel(N), body.frame.ang_vel_in(N)] elif isinstance(body, Particle): vlist = [body.point.vel(N)] else: raise TypeError("The body list may only contain either " "RigidBody or Particle as list elements.") v = [vel.subs(self._qdot_u_map) for vel in vlist] return partial_velocity(v, self.u, N)
def get_partial_velocity(body): if isinstance(body, RigidBody): vlist = [body.masscenter.vel(N), body.frame.ang_vel_in(N)] elif isinstance(body, Particle): vlist = [body.point.vel(N),] else: raise TypeError('The body list may only contain either ' 'RigidBody or Particle as list elements.') v = [msubs(vel, self._qdot_u_map) for vel in vlist] return partial_velocity(v, self.u, N)
def test_partial_velocity(): q1, q2, q3, u1, u2, u3 = dynamicsymbols('q1 q2 q3 u1 u2 u3') u4, u5 = dynamicsymbols('u4, u5') r = symbols('r') N = ReferenceFrame('N') Y = N.orientnew('Y', 'Axis', [q1, N.z]) L = Y.orientnew('L', 'Axis', [q2, Y.x]) R = L.orientnew('R', 'Axis', [q3, L.y]) R.set_ang_vel(N, u1 * L.x + u2 * L.y + u3 * L.z) C = Point('C') C.set_vel(N, u4 * L.x + u5 * (Y.z ^ L.x)) Dmc = C.locatenew('Dmc', r * L.z) Dmc.v2pt_theory(C, N, R) vel_list = [Dmc.vel(N), C.vel(N), R.ang_vel_in(N)] u_list = [u1, u2, u3, u4, u5] assert (partial_velocity(vel_list, u_list, N) == [[ -r * L.y, r * L.x, 0, L.x, cos(q2) * L.y - sin(q2) * L.z ], [0, 0, 0, L.x, cos(q2) * L.y - sin(q2) * L.z], [L.x, L.y, L.z, 0, 0]])
def test_partial_velocity(): q1, q2, q3, u1, u2, u3 = dynamicsymbols('q1 q2 q3 u1 u2 u3') u4, u5 = dynamicsymbols('u4, u5') r = symbols('r') N = ReferenceFrame('N') Y = N.orientnew('Y', 'Axis', [q1, N.z]) L = Y.orientnew('L', 'Axis', [q2, Y.x]) R = L.orientnew('R', 'Axis', [q3, L.y]) R.set_ang_vel(N, u1 * L.x + u2 * L.y + u3 * L.z) C = Point('C') C.set_vel(N, u4 * L.x + u5 * (Y.z ^ L.x)) Dmc = C.locatenew('Dmc', r * L.z) Dmc.v2pt_theory(C, N, R) vel_list = [Dmc.vel(N), C.vel(N), R.ang_vel_in(N)] u_list = [u1, u2, u3, u4, u5] assert (partial_velocity(vel_list, u_list, N) == [[- r*L.y, r*L.x, 0, L.x, cos(q2)*L.y - sin(q2)*L.z], [0, 0, 0, L.x, cos(q2)*L.y - sin(q2)*L.z], [L.x, L.y, L.z, 0, 0]])