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, Kane, Lagrange, ...)
- 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.
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