def test_model(self):
np.testing.assert_array_less(
SurfaceGuidedMassSystem(
surface=EllipticParaboloid(1.0, 2.0),
s0=nprand((4,)),
solid=1.0,
forces=[
Gravity(1.0, [0, 0, -10.0]),
SpringForce(1.0, [0.0, 0.0, 0.0]),
ViscousFriction(2.0),
],
).solve(time=np.linspace(0, 20, 1000))[-1,:],
1e-5*np.ones((4,))
)
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
import numpy as np
# model
sphere = Sphere(1.0)
m = 1.0
g = np.array([-1.0, 0.0, 0.0])
k = 1.0
clip = np.array([0.0, 0.0, 1.0])
system = SurfaceGuidedMassSystem(
surface=sphere,
s0=np.array([np.pi/2, 1.0, np.pi/2, 0.0]),
m=m,
forces=[
Gravity(m=m, g=g),
SpringForce(stiffness=k, clip=clip),
# ViscousFriction(mu=0.2),
]
)
# simulate
time = np.linspace(0, 20, 5000)
states = system.solve(time)
# build (todo opti)
mesh = sphere.build_surface(*sphere.mesh(50, 50))
physics = system.solutions(states, time)
# initial values
x0, vx0 = 2.0, 0.0
y0, vy0 = 0.0, 4.0
# model
plan = Plan.from_xz_rotation(angle=0.0).setlims(-2, 2.5, -3.5, 5).multlims(1)
m = 1.0
system = SurfaceGuidedMassSystem(
surface=plan,
s0=np.array([x0, vx0, y0, vy0]),
m=m,
forces=[
Gravity(m=m, g=np.array([0.0, 0.0, -9.81])),
LengthedSpringForce(stiffness=1.0,
clip=np.array([0.0, 0.0, 0.0]),
l0=1.0),
ViscousFriction(mu=0.15), # test for mu=0.2 and 0.8
])
# simulation
time = np.linspace(0, 60, 6000)
states = system.solve(time)
physics = system.solutions(states, time)
trajectory = physics[:, Pi]
speed = physics[:, Vi]
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])])
from gsurface import Plan, NewtonGravity, SurfaceGuidedMassSystem, Tyi, build_s0, ViscousFriction
from gsurface.plotter import mayavi_plot_surfaces, SurfacePlot, matplotlib_plot_solutions
import numpy as np
# simulate a planet rotating around a fixed massive system
universe_def = Plan(c=1.0).setlims(u_ul=2.5, v_ul=2)
universe = universe_def.build_surface(*universe_def.mesh(50, 50))
model = SurfaceGuidedMassSystem(
surface=universe_def,
s0=build_s0(u0=1.0, dv0=0.5, du0=1.0),
m=1.0,
forces=[
NewtonGravity(m=1.0, M=100.0, G=1.0, clip=np.zeros((3, ))),
# DistanceGravity(m=1.0, M=100.0, G=1.0, clip=np.array([1.0, 0.0, 0.0])), # 2 mass objects
# ViscousFriction(0.1) # friction
])
time = np.linspace(0, 20, 3000)
data = model.solve(time)
solutions = model.solutions(data, time)
matplotlib_plot_solutions(time, data, solutions)
mayavi_plot_surfaces([SurfacePlot(universe, trajectory=solutions[Tyi])])
sphere = Sphere(0.5).multlims(0.5).translate(np.array([1.0, 2.0, 0.0])).rotate(
Rotation.from_rotvec([0.0, 1.0, 2.0]).as_matrix())
tore = Tore()
cat = Catenoid()
forces = [
StaticFieldElectroMagneticForce(1.0, np.array([1.0, 2.0, 3.0])),
SpringForce(),
ViscousFriction(),
Gravity(),
Gravity() + NewtonGravity()
]
model1 = SurfaceGuidedMassSystem(surface=sphere,
forces=forces,
solid=23.0,
s0=build_s0(1.0, 2.0, 3.0, 4.0))
structure = TriangleStructure(23.0, 1.0, 23.0, 4.3)
structure[0, 2].mu = 2.0
structure[0, 1].mu = 3.0
structure[1, 2].mu = 4.0
model2 = SurfaceGuidedStructureSystem(sphere,
structure,
structureForces=forces)
objects = model1
# print(surfaces)
save(filename, objects, 4)
# saveB64(filename + "b64", objects)
# queue of N solids, attached with a spring
SYSTEMS = 8
stiffness = 10
tore = Tore(0.5, 1.0)
tore_mesh = tore.build_surface(*tore.mesh(50, 50))
# build model
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)]
import numpy as np
from mayavi import mlab
from gsurface import SurfaceGuidedMassSystem, SpringForce, Gravity, \
ViscousFriction, build_s0
from gsurface.indexes import *
from gsurface.plotter import matplotlib_plot_solutions, mayavi_animate_surface_trajectory
from gsurface.surface import Tore
m = 1.0
system = SurfaceGuidedMassSystem(
surface=Tore(0.5, 1.0),
s0=build_s0(u0=0.0, du0=0.5, v0=1.0, dv0=0.0),
m=m,
forces=[
SpringForce(stiffness=5.0, clip=np.array([0.0, 0.0, 0.0])),
Gravity(m=m, g=np.array([0.0, 0.0, -2.0])),
# LengthedSpringForce(stiffness=5.0, clip=np.array([1.0, 1.0, 0.0]), l0=1.0),
ViscousFriction(mu=0.5),
])
# simulate
time = np.linspace(0, 10, 5000)
states = system.solve(time)
mesh = system.surface.mesh(100, 100)
smesh = system.surface.build_surface(*mesh)
physics = system.solutions(states, time)
dvvz=-u * np.sin(u - v),
)
surface = NewSurface().multlims(1.5)
surface.check_verbose(20, 20)
from gsurface import SurfaceGuidedMassSystem, Tyi, build_s0
from gsurface.forces import ViscousFriction, SpringForce
model = SurfaceGuidedMassSystem(
surface=surface,
s0=build_s0(u0=2.5, du0=-8.0, dv0=5.0),
m=1.0,
forces=[
SpringForce(10.0),
ViscousFriction(1.0)
]
)
from gsurface.plotter import mayavi_plot_surfaces, SurfacePlot
surface = NewSurface()
surface_mesh = surface.build_surface(*surface.mesh(50, 50))
time = np.linspace(0, 10, 1000)
data = model.solve(time)