Vector operations

• Notation: Syntactical form, constructors, RigidFrame, RigidBody.
• Addition/negation/subtraction: Computation, uniform basis, mixed basis.
• Dot and Cross: Command syntax, functions for calculating angles, distances, area, volume, ...
• Ordinary time-derivative: Command syntax, need for a reference frame in computation.
• Partial derivative: Command syntax, possible need for a reference frame in computation.

Rotational kinematics

• Rotation matrix: Syntactical form, simple rotation matrix, successive rotations, matrix multiplication, command syntax, automated computation with syntactical forms.
• Angular velocity: Syntactical form, simple angular velocity, angular addition theorem, use with vector differentiation, command syntax, automated computation with syntactical forms.
• Angular acceleration: Syntactical form, definition, utility in formulas, command syntax, automated computation with syntactical forms.
• Rotational Odes: Euler angles, Euler parameters, Rodrigues parameters, Poisson parameters.

Translational kinematics

• Position vector: Syntactical form, command syntax, automatic computation.
• Velocity: Syntactical form, formulas for forming velocity, computation.
• Acceleration: Syntactical form, formulas for forming acceleration, command syntax, automated computation with syntactical forms.

Mass distribution

• Mass: Assigning mass of particles and bodies. Summing mass of particles, bodies, and systems.
• Mass center: Syntax for body's center of mass. Calculating position, velocity, and acceleration of system mass centers.
• Inertia properties: Assigning rigid body's via inertia dyadics, matrices, moments, and products. Calculating system inertia properties (dyadics, matrices, moments, products, and radii of gyration).

Force, torque, moment, power, work, and energy

• Force: Syntactical form. Command syntax for adding forces to points. Command syntax for summing forces on points, particles, bodies, frames, and systems. Force models for gravity (local/universal), electrostatics, springs, dampers, etc.
• Torque: Syntactical form. Command syntax for adding torque to reference frames. Torque models for viscous dampers, etc.
• Moment: Command syntax for summing moments of forces on points, particles, bodies, frames, and systems about a designated point.
• Power/work: Calculating system power and work done by dissipative forces.
• Energy: Commands for kinetic/potential energy and energy checking functions.

Statics and dynamics

• Translation: Command syntax for statics or dynamics using forces or Newton's equations for points, particles, bodies, frames, and systems.
• Rotation: Command syntax for statics or dynamics using moments or Euler's equations (angular momentum principle) for points, particles, bodies, frames, and systems.
• System: Command syntax for statics or dynamics of systems using generalized methods, e.g., Kane and Lagrange.

Simulation and code generation (C, Fortran, MATLABŪ, ...)

• Linear algebraic equations: Solve, Input, Output, Units, and UnitSystem.
• Nonlinear algebraic equations: Solve, initial guesses and convergence.
• Nonlinear differential equations: Integration step, error tolerances, checking functions, graphing.

Constraints (part of 3⁺ day course)

• Augmented method: Augmenting constraints to equations of motion. Initial configuration and motion problems.
• Embedded method: Determination of independent and dependent variables.
• Mixed methods: Constrained systems with augmented and embedded constraints.

Efficiency (part of 3⁺ day course)

• Configuration variables: Generating efficient simulation and control-systems codes.
• Motion variables: Choice of angular velocity variables, generalized speeds, and independent/dependent subsets.
• AutoZee: Automating the introduction of efficient intermediate variables.

Linearization and control-system integration (part of 3⁺ day course)

• Linearization: Nominal solutions, perturbations.
• Efficient linearization: Efficient generation of linearized equations of motion.
• Stability analysis: Eigenvalues, eigenvectors, system response.
• Control system design: State-space feedback control techniques.