MotionGenesis: F=ma Software, textbooks, training, consulting.
Force, mass, motion, and energy

Vectors, tensors, and geometry
  • Commands for calculating angles, distances, and unit vectors.
  • Creates vectors and dyadics (tensors) through special constructors.
  • Multi-basis capable dot-products and cross-products.
  • Calculates ordinary and partial derivatives of vectors (accounts for change in both magnitude and direction)
  • Uses the symbol   >   to clearly distinguish vectors from scalars.
  • Built-in zero vector, zero dyadic, and unit dyadic, i.e.,   0>   0>>   1>>
Rotational kinematics
  • Easy-to-use Rotate command sets rotation matrix, angular velocity, angular acceleration.
  • Individual commands to SetRotationMatrix, SetAngularVelocity, or SetAngularAcceleration,
  • Automatically calculates rotation matrices, angular velocities, and angular accelerations.
  • Commands for calculating angles between vectors or unit vectors.
  • Forward kinematics, inverse kinematics, and mixed problems.
Translational kinematics
  • Easy-to-use Translate command sets position, velocity, acceleration.
  • Individual commands to SetPosition, SetVelocity, or SetAcceleration,
  • Automatically calculates position vectors, velocities, and accelerations.
  • Commands for calculating distance (length) and speed.
  • Forward kinematics, inverse kinematics, and mixed problems.
Statics and dynamics   (Newton/Euler, D'Alembert, and Kane)
  • GetStatics sums forces and moments for static ("free-body") analysis.
  • GetDynamics automates Newton/Euler (D'Alembert) dynamics.
  • GetStaticsKane and GetDynamicsKane eliminate constraint forces for efficient analyses.
  • Forms linear momentum, angular momentum, and kinetic energy.
  • Employs highly efficient algorithms to formulate and solve equations of motion.
  • Provides special algorithms for dealing with systems involving gyrostats.
  • Produces nonlinear and linearized equations of motion for simulation, design, and control systems.
  • Forward dynamics, inverse dynamics, and mixed problems.
Force and torque
  • Easy-to-use AddForce and AddTorque commands and commands to sum forces and moments.
  • Simple commands to add forces from springs, dampers, electrostatics, gravity, linear actuations, etc.
  • Implements Newton's law of action/reaction for forces and torques.
  • Efficiently calculates generalized forces.
Kinetic energy, potential energy, power, and work
  • Calculates kinetic energy for a particle, rigid body, or system.
  • Calculates gravitational and spring potential energies.
  • Calculates system power and facilitates calculating work from dissipative forces.
  • Efficient energy integral for checking numerical integration accuracy.
  • Calculates kinetic energy of degree 0, 1, or 2 for Hamiltonian.
Mass, center of mass, inertia, and charge
  • Easy-to-use SetMass, SetInertia, and SetCharge commands.
  • Calculates mass, center of mass, and inertia properties of sets of objects.
  • Calculates moments/products of inertia, radii of gyration, and other inertia properties.
  • Calculates the position, velocity, and acceleration of the mass center of sets of objects.
Advanced methods and constraints
  • Employs augmented or embedded constraints.
  • Commands for enforcing linear/nonlinear constraints with proper initial values.
  • Commands for enforcing constraints and their time-derivatives.
  • Introduces intermediate variables for fast, efficient, compact code.
MotionGenesis Software Feature Physics (photo courtesy of OpenSim)
Photo courtesy of OpenSim

MotionGenesis: F=ma Software, textbooks, training, consulting.

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