def test_auto_vel_derivative(): q1, q2 = dynamicsymbols('q1:3') u1, u2 = dynamicsymbols('u1:3', 1) A = ReferenceFrame('A') B = ReferenceFrame('B') C = ReferenceFrame('C') B.orient_axis(A, A.z, q1) B.set_ang_vel(A, u1 * A.z) C.orient_axis(B, B.z, q2) C.set_ang_vel(B, u2 * B.z) Am = Point('Am') Am.set_vel(A, 0) Bm = Point('Bm') Bm.set_pos(Am, B.x) Bm.set_vel(B, 0) Bm.set_vel(C, 0) Cm = Point('Cm') Cm.set_pos(Bm, C.x) Cm.set_vel(C, 0) temp = Cm._vel_dict.copy() assert Cm.vel(A) == (u1 * B.y + (u1 + u2) * C.y) Cm._vel_dict = temp Cm.v2pt_theory(Bm, B, C) assert Cm.vel(A) == (u1 * B.y + (u1 + u2) * C.y)
def test_auto_point_vel_if_tree_has_vel_but_inappropriate_pos_vector(): q1, q2 = dynamicsymbols('q1 q2') B = ReferenceFrame('B') S = ReferenceFrame('S') P = Point('P') P.set_vel(B, q1 * B.x) P1 = Point('P1') P1.set_pos(P, S.y) raises(ValueError, lambda: P1.vel(B)) # P1.pos_from(P) can't be expressed in B raises(ValueError, lambda: P1.vel(S)) # P.vel(S) not defined
def test_point_vel(): #Basic functionality q1, q2 = dynamicsymbols('q1 q2') N = ReferenceFrame('N') B = ReferenceFrame('B') Q = Point('Q') O = Point('O') Q.set_pos(O, q1 * N.x) raises(ValueError, lambda: Q.vel(N)) # Velocity of O in N is not defined O.set_vel(N, q2 * N.y) assert O.vel(N) == q2 * N.y raises(ValueError, lambda: O.vel(B)) #Velocity of O is not defined in B
def test_auto_vel_dont_overwrite(): t = dynamicsymbols._t q1, q2, u1 = dynamicsymbols('q1, q2, u1') N = ReferenceFrame('N') P = Point('P1') P.set_vel(N, u1 * N.x) P1 = Point('P1') P1.set_pos(P, q2 * N.y) assert P1.vel(N) == q2.diff(t) * N.y + u1 * N.x assert P.vel(N) == u1 * N.x P1.set_vel(N, u1 * N.z) assert P1.vel(N) == u1 * N.z
def test_auto_point_vel_connected_frames(): t = dynamicsymbols._t q, q1, q2, u = dynamicsymbols('q q1 q2 u') N = ReferenceFrame('N') B = ReferenceFrame('B') O = Point('O') O.set_vel(N, u * N.x) P = Point('P') P.set_pos(O, q1 * N.x + q2 * B.y) raises(ValueError, lambda: P.vel(N)) N.orient(B, 'Axis', (q, B.x)) assert P.vel( N) == (u + q1.diff(t)) * N.x + q2.diff(t) * B.y - q2 * q.diff(t) * B.z
def test_auto_point_vel_multiple_paths_warning_arises(): q, u = dynamicsymbols('q u') N = ReferenceFrame('N') O = Point('O') P = Point('P') Q = Point('Q') R = Point('R') P.set_vel(N, u * N.x) Q.set_vel(N, u * N.y) R.set_vel(N, u * N.z) O.set_pos(P, q * N.z) O.set_pos(Q, q * N.y) O.set_pos(R, q * N.x) with warnings.catch_warnings( ): #There are two possible paths in this point tree, thus a warning is raised warnings.simplefilter("error") raises(UserWarning, lambda: O.vel(N))
def test_auto_vel_multiple_path_warning_msg(): N = ReferenceFrame('N') O = Point('O') P = Point('P') Q = Point('Q') P.set_vel(N, N.x) Q.set_vel(N, N.y) O.set_pos(P, N.z) O.set_pos(Q, N.y) with warnings.catch_warnings( record=True ) as w: #There are two possible paths in this point tree, thus a warning is raised warnings.simplefilter("always") O.vel(N) assert issubclass(w[-1].category, UserWarning) assert 'Velocity automatically calculated based on point' in str( w[-1].message) assert 'Velocities from these points are not necessarily the same. This may cause errors in your calculations.' in str( w[-1].message)
def test_auto_vel_cyclic_warning_arises(): P = Point('P') P1 = Point('P1') P2 = Point('P2') P3 = Point('P3') N = ReferenceFrame('N') P.set_vel(N, N.x) P1.set_pos(P, N.x) P2.set_pos(P1, N.y) P3.set_pos(P2, N.z) P1.set_pos(P3, N.x + N.y) with warnings.catch_warnings( ): #The path is cyclic at P1, thus a warning is raised warnings.simplefilter("error") raises(UserWarning, lambda: P2.vel(N))
def test_auto_vel_cyclic_warning_msg(): P = Point('P') P1 = Point('P1') P2 = Point('P2') P3 = Point('P3') N = ReferenceFrame('N') P.set_vel(N, N.x) P1.set_pos(P, N.x) P2.set_pos(P1, N.y) P3.set_pos(P2, N.z) P1.set_pos(P3, N.x + N.y) with warnings.catch_warnings( record=True ) as w: #The path is cyclic at P1, thus a warning is raised warnings.simplefilter("always") P2.vel(N) assert issubclass(w[-1].category, UserWarning) assert 'Kinematic loops are defined among the positions of points. This is likely not desired and may cause errors in your calculations.' in str( w[-1].message)
def test_auto_point_vel_multiple_point_path(): t = dynamicsymbols._t q1, q2 = dynamicsymbols('q1 q2') B = ReferenceFrame('B') P = Point('P') P.set_vel(B, q1 * B.x) P1 = Point('P1') P1.set_pos(P, q2 * B.y) P1.set_vel(B, q1 * B.z) P2 = Point('P2') P2.set_pos(P1, q1 * B.z) P3 = Point('P3') P3.set_pos(P2, 10 * q1 * B.y) assert P3.vel(B) == 10 * q1.diff(t) * B.y + (q1 + q1.diff(t)) * B.z
def test_auto_point_vel(): t = dynamicsymbols._t q1, q2 = dynamicsymbols('q1 q2') N = ReferenceFrame('N') B = ReferenceFrame('B') O = Point('O') Q = Point('Q') Q.set_pos(O, q1 * N.x) O.set_vel(N, q2 * N.y) assert Q.vel(N) == q1.diff(t) * N.x + q2 * N.y # Velocity of Q using O P1 = Point('P1') P1.set_pos(O, q1 * B.x) P2 = Point('P2') P2.set_pos(P1, q2 * B.z) raises(ValueError, lambda: P2.vel(B) ) # O's velocity is defined in different frame, and no #point in between has its velocity defined raises(ValueError, lambda: P2.vel(N)) # Velocity of O not defined in N
def test_auto_point_vel_shortest_path(): t = dynamicsymbols._t q1, q2, u1, u2 = dynamicsymbols('q1 q2 u1 u2') B = ReferenceFrame('B') P = Point('P') P.set_vel(B, u1 * B.x) P1 = Point('P1') P1.set_pos(P, q2 * B.y) P1.set_vel(B, q1 * B.z) P2 = Point('P2') P2.set_pos(P1, q1 * B.z) P3 = Point('P3') P3.set_pos(P2, 10 * q1 * B.y) P4 = Point('P4') P4.set_pos(P3, q1 * B.x) O = Point('O') O.set_vel(B, u2 * B.y) O1 = Point('O1') O1.set_pos(O, q2 * B.z) P4.set_pos(O1, q1 * B.x + q2 * B.z) with warnings.catch_warnings( ): #There are two possible paths in this point tree, thus a warning is raised warnings.simplefilter('error') with ignore_warnings(UserWarning): assert P4.vel( B) == q1.diff(t) * B.x + u2 * B.y + 2 * q2.diff(t) * B.z