def exercise_basic():
assert approx_equal(sum(spatial_lib.xrot((1, 2, 3, 4, 5, 6, 7, 8, 9))), 90)
assert approx_equal(sum(spatial_lib.xtrans((1, 2, 3))), 6)
assert approx_equal(
sum(
spatial_lib.cb_as_spatial_transform(cb=matrix.rt(((1, 2, 3, 4, 5,
6, 7, 8, 9),
(1, 2, 3))))),
90)
assert approx_equal(sum(spatial_lib.crm((1, 2, 3, 4, 5, 6))), 0)
assert approx_equal(sum(spatial_lib.crf((1, 2, 3, 4, 5, 6))), 0)
i_spatial = spatial_lib.mci(m=1.234,
c=matrix.col((1, 2, 3)),
i=matrix.sym(sym_mat3=(2, 3, 4, 0.1, 0.2,
0.3)))
assert approx_equal(sum(i_spatial), 21.306)
assert approx_equal(
spatial_lib.kinetic_energy(i_spatial=i_spatial,
v_spatial=matrix.col((1, 2, 3, 4, 5, 6))),
75.109)
#
mass_points = body_lib.mass_points(sites=matrix.col_list([
(0.949, 2.815, 5.189), (0.405, 3.954, 5.917), (0.779, 5.262, 5.227)
]),
masses=[2.34, 3.56, 1.58])
assert approx_equal(mass_points.sum_of_masses(), 7.48)
assert approx_equal(mass_points.center_of_mass(),
[0.654181818182, 3.87397058824, 5.54350802139])
assert approx_equal(mass_points._sum_of_masses, 7.48)
assert approx_equal(
mass_points.inertia(pivot=matrix.col((0.9, -1.3, 0.4))), [
404.7677928, 10.04129606, 10.09577652, 10.04129606, 199.7384559,
-199.3511949, 10.09577652, -199.3511949, 206.8314171
])
def exercise_basic():
assert approx_equal(sum(spatial_lib.xrot((1,2,3,4,5,6,7,8,9))), 90)
assert approx_equal(sum(spatial_lib.xtrans((1,2,3))), 6)
assert approx_equal(
sum(spatial_lib.cb_as_spatial_transform(
cb=matrix.rt(((1,2,3,4,5,6,7,8,9), (1,2,3))))), 90)
assert approx_equal(sum(spatial_lib.crm((1,2,3,4,5,6))), 0)
assert approx_equal(sum(spatial_lib.crf((1,2,3,4,5,6))), 0)
i_spatial = spatial_lib.mci(
m=1.234,
c=matrix.col((1,2,3)),
i=matrix.sym(sym_mat3=(2,3,4,0.1,0.2,0.3)))
assert approx_equal(sum(i_spatial), 21.306)
assert approx_equal(spatial_lib.kinetic_energy(
i_spatial=i_spatial, v_spatial=matrix.col((1,2,3,4,5,6))), 75.109)
#
mass_points = body_lib.mass_points(
sites=matrix.col_list([
(0.949, 2.815, 5.189),
(0.405, 3.954, 5.917),
(0.779, 5.262, 5.227)]),
masses=[2.34, 3.56, 1.58])
assert approx_equal(mass_points.sum_of_masses(), 7.48)
assert approx_equal(mass_points.center_of_mass(),
[0.654181818182, 3.87397058824, 5.54350802139])
assert approx_equal(mass_points._sum_of_masses, 7.48)
assert approx_equal(
mass_points.inertia(pivot=matrix.col((0.9,-1.3,0.4))),
[404.7677928, 10.04129606, 10.09577652,
10.04129606, 199.7384559, -199.3511949,
10.09577652, -199.3511949, 206.8314171])
def e_kin(O):
"RBDA Eq. 2.67, p. 35"
if (O.__e_kin is None):
result = 0
for body,v in zip(O.bodies, O.spatial_velocities()):
result += kinetic_energy(i_spatial=body.i_spatial, v_spatial=v)
O.__e_kin = result
return O.__e_kin
def e_kin(O):
"RBDA Eq. 2.67, p. 35"
if (O.__e_kin is None):
result = 0
for body, v in zip(O.bodies, O.spatial_velocities()):
result += kinetic_energy(i_spatial=body.i_spatial, v_spatial=v)
O.__e_kin = result
return O.__e_kin
def qd_e_kin_scales(O, e_kin_epsilon=1.e-12):
result = []
rap = result.append
for body,asi in zip(O.bodies, O.accumulated_spatial_inertia()):
s = body.joint.motion_subspace
j_dof = body.joint.degrees_of_freedom
qd = [0] * j_dof
for i in xrange(j_dof):
qd[i] = 1
vj = matrix.col(qd)
qd[i] = 0
if (s is not None): vj = s * vj
e_kin = kinetic_energy(i_spatial=asi, v_spatial=vj)
if (e_kin < e_kin_epsilon):
rap(1)
else:
rap(1 / e_kin**0.5)
return result
def qd_e_kin_scales(O, e_kin_epsilon=1.e-12):
result = []
rap = result.append
for body, asi in zip(O.bodies, O.accumulated_spatial_inertia()):
s = body.joint.motion_subspace
j_dof = body.joint.degrees_of_freedom
qd = [0] * j_dof
for i in xrange(j_dof):
qd[i] = 1
vj = matrix.col(qd)
qd[i] = 0
if (s is not None): vj = s * vj
e_kin = kinetic_energy(i_spatial=asi, v_spatial=vj)
if (e_kin < e_kin_epsilon):
rap(1)
else:
rap(1 / e_kin**0.5)
return result
