code: def test_box_on_ground(self):
      # Particle sliding on ground with friction. The applied force is assumed
      # to be positive and to be higher than the friction force.
      g, m, mu = symbols("g m mu")
      q, u, ua = dynamicsymbols("q u ua")
      N, F = dynamicsymbols("N F", positive=True)
      P = Particle("P", mass=m)
      system = System()
      system.add_bodies(P)
      P.masscenter.set_pos(system.fixed_point, q * system.x)
      P.masscenter.set_vel(system.frame, u * system.x + ua * system.y)
      system.q_ind, system.u_ind, system.u_aux = [q], [u], [ua]
      system.kdes = [q.diff(t) - u]
      system.apply_uniform_gravity(-g * system.y)
      system.add_loads(
          Force(P, N * system.y),
          Force(P, F * system.x - mu * N * system.x),
      )
      system.validate_system()
      system.form_eoms()
  
      # Test other output
      Mk = ImmutableMatrix([1])
      gk = ImmutableMatrix([u])
      Md = ImmutableMatrix([m])
      gd = ImmutableMatrix([F - mu * N])
      Mm = (Mk.row_join(zeros(1, 1))).col_join(zeros(1, 1).row_join(Md))
      gm = gk.col_join(gd)
      aux_eqs = ImmutableMatrix([N - m * g])
      assert simplify(system.mass_matrix - Md) == zeros(1, 1)
      assert simplify(system.forcing - gd) == zeros(1, 1)
      assert simplify(system.mass_matrix_full - Mm) == zeros(2, 2)
      assert simplify(system.forcing_full - gm) == zeros(2, 1)
      assert simplify(
          system.eom_method.auxiliary_eqs - aux_eqs
      ) == zeros(1, 1)
  
imports: import pytest
  from sympy.core.symbol import symbols
  from sympy.core.sympify import sympify
  from sympy.functions.elementary.trigonometric import cos, sin
  from sympy.matrices.dense import eye, zeros
  from sympy.matrices.immutable import ImmutableMatrix
  from sympy.physics.mechanics import Force, KanesMethod, LagrangesMethod, Particle, PinJoint, Point, PrismaticJoint, ReferenceFrame, RigidBody, Torque, TorqueActuator, System, dynamicsymbols
  from sympy.simplify.simplify import simplify
  from sympy.solvers.solvers import solve
label_desc: Use image node_id 3 for calling the TestSystemExamples obj's underlying member method code with example usage: obj.test_box_on_ground() without return types