# ODE model
def ds(S: np.ndarray, t: float):
dS = np.zeros_like(S)
X = S[::2]
V = S[1::2]
dS[0::2] = V
dS[1::2] = forces.eval(t, X, V) / mass
return dS
# initial state
s0 = np.array([
0.1,
0.2,
0.0,
1.5,
0.0,
0.0 # x, vx, y, vy, z, vz
])
time = np.linspace(0, 10, 2000)
states = odeint(ds, s0, time)
mayavi_plot_surfaces([SurfacePlot(trajectory=states[:, ::2], animate=True)])
mlab.view(0.0, 90.0, 5.0)
from gsurface import Plan, SurfaceGuidedMassSystem, build_s0
from gsurface.forces import CenterDirectedViscousFriction, ConstantDirectedViscousFriction
from gsurface.forces import SpringDampingForce
from gsurface.plotter import mayavi_plot_surfaces, SurfacePlot, Tyi
# simulate a 2D spring damping system, we notice that the radial speed tends to 0 where rotational speed still constant
plan = Plan(a=0.0, c=1.0)
surface = plan.build_surface(*plan.mesh(50, 50))
model = SurfaceGuidedMassSystem(surface=plan,
s0=build_s0(u0=0.5, du0=0.0, dv0=5),
m=1.0,
forces=[
ConstantDirectedViscousFriction(
1.0, np.array([1.0, 0.0, 0.0])),
CenterDirectedViscousFriction(1.0),
SpringDampingForce(100.0, 1.0, None, 1.0)
])
time = np.linspace(0, 10, 3000)
data = model.solve(time)
solutions = model.solutions(data, time)
mayavi_plot_surfaces([SurfacePlot(surface, trajectory=solutions[Tyi])])
from gsurface.serialize import save_attached
model_parsed = save_attached(model, __file__)
import numpy as np
from gsurface import SurfaceGuidedMassSystem, build_s0
from gsurface.forces import Gravity, SpringForce, ViscousFriction
from gsurface.plotter import mayavi_plot_surfaces, SurfacePlot, Tyi
from gsurface.surface import Cylinder
mass = 1.0 # kg
system = SurfaceGuidedMassSystem(
surface=Cylinder(R=1.0).setlims(v_ll=-1, v_ul=1),
solid=mass,
forces=Gravity(mass, g=np.array([0.0, 0.0, -1.0])) +
SpringForce(stiffness=1.0, clip=np.array([-0.5, 0.0, 0.0])) +
ViscousFriction(0.1),
s0=build_s0(0, 0.5, 0, 0),
)
time = np.linspace(0, 50.0, 1000)
data = system.solve(time)
solutions = system.solutions(data, time)
smesh = system.surface.build_surface(*system.surface.mesh(40, 40))
mayavi_plot_surfaces(
[SurfacePlot(smesh, showSurface=True, trajectory=solutions[Tyi])])
joint_sim = SurfaceGuidedInteractedMassSystems([
SurfaceGuidedMassSystem(surface=tore,
s0=build_s0(0, 2 * j, 0.0, 1 + j),
m=1.0,
forces=[
ViscousFriction(0.2),
Gravity(1.0, np.array([0.0, 0.0, -1.0]))
]) for j in range(SYSTEMS)
], {(i, i + 1): SpringInteraction(1.0)
for i in range(SYSTEMS - 1)})
time = np.linspace(0, 25, 2000)
data = joint_sim.solve(time)
solutions = joint_sim.solutions(data, time)
colors = [(1, 0, 0), (0, 1, 0), (0, 0, 1), (1, 1, 0), (1, 0, 1), (0, 1, 0),
(0, 1, 1), (1, 1, 1)]
NCOLORS = len(colors)
mayavi_plot_surfaces([
SurfacePlot(
tore_mesh, # surface
i == 0,
trajectory=solution[Tyi],
trajectoryColor=colors[i % NCOLORS],
showTrajectory=True) for i, solution in enumerate(solutions)
])
# check surface definition
print(para, para.check(20, 20))
# create model
model = SurfaceGuidedMassSystem(surface=para,
s0=s0,
m=1.0,
forces=[
Gravity(m=1.0, g=np.array([0.0, 0.0, -2])),
ViscousFriction(mu=0.5)
])
# solve
time = np.linspace(0, 20, 2000)
data = model.solve(time)
# calculate other physics quantities
solutions = model.solutions(data, time)
trajectory = solutions[Tyi]
# plot
matplotlib_plot_solutions(time, data, solutions)
mayavi_plot_surfaces(
[SurfacePlot(surface, trajectory=trajectory, animate=True)])
mlab.view(0, 30, 5.0, np.zeros((3, )))
from gsurface import Tyi
from gsurface.advanced.structure import SurfaceGuidedStructureSystem, TriangleStructure
from gsurface.forces import ViscousFriction
from gsurface.plotter import mayavi_plot_surfaces, SurfacePlot, mlab
from gsurface.surface import Plan
surface = Plan(0.0, 0.0, 1.0)
mesh = surface.build_surface(*surface.mesh(50, 50))
structure = TriangleStructure(totalMass=4.0, stiffness=1000.0, mu=10.0, l0=0.5)
structure[1, 2].l0 = 0.8
structure.nodes[0].mass = 100.0
model = SurfaceGuidedStructureSystem(surface,
structure,
structureForces=[ViscousFriction(1.0)])
time = np.linspace(0, 2, 1000)
states = model.solve(time)
solutions = list(model.solutions(states, time))
mayavi_plot_surfaces([
SurfacePlot(mesh, showSurface=(i == 0), trajectory=solutions[i][Tyi][::5])
for i in range(model.degree)
])
mlab.view(0, 0, 5.0, np.zeros((3, )))
surface = Tore(0.5, 1.0)
mesh = surface.build_surface(*surface.mesh(50, 50))
snake = BowStructure(SIZE, 1.0, stiffness=1000.0, mu=10.0, l0=1.0)
snake.interactions[(0, SIZE - 1)].stiffness = 100.0
sim = SurfaceGuidedStructureSystem(surface, snake, s0=nprand(4*SIZE), structureForces=[
ViscousFriction(0.01)
])
sim.s0[1::4] = 1.0
time = np.linspace(0, 40, 1000)
data = sim.solve(time)
solutions = sim.solutions(data, time)
model_parsed = save_attached(sim, __file__)
mayavi_plot_surfaces([
SurfacePlot(
smesh=mesh,
showSurface= i == 0,
trajectory=solution[Tyi],
trajectoryColor=rgb[i % len(rgb)],
showTrajectory=True
) for i, solution in enumerate(solutions)
])
