Design#
This library is motivated by a need for flight dynamics models encoded as simple systems of differential equations:
(where \(\vec{x}\) is a vector of state variables and \(\vec{u}\) is a vector of system inputs).
[[Typical aircraft simulators expose a complicated model interface, making them difficult to use and extend. Instead, deliberately targeting numerical derivatives makes the flight dynamics models directly usable in common applications such as control modeling and statistical filtering.]]
Background#
This library began as an implementation of my thesis: Parametric Paraglider Modeling. Its motivation was to enable statistical flight reconstruction of the wind fields present during recorded paraglider flights. The task would require a flight dynamics model of the glider that produced the flight record, so the objective of the paper was to estimate the flight dynamics of commercial paraglider wings using only basic technical data. Achieving that objective required decomposing the paraglider system into components that enabled convenient model parametrizations. Although development focused on paraglider dynamics, the model decomposition makes the library suitable for general gliding aircraft such as kites and hang gliders.
Design overview#
Creating a flight dynamics model using this library means implementing
a StateDynamics class that
defines a set of state variables and computes numerical state derivatives that
can be integrated over time to produce a flight trajectory.
Because gliding aircraft are complex systems, it is easier to estimate their dynamics if they are decomposed into composite models, leading to a natural hierarchy that builds up to the state dynamics to record the behavior of the system.
Model hierarchy#
The models in this library can be categorized into three groups:
Components
Systems
State variables
Components#
Component models define the control inputs of the individual components of the glider system, their inertial properties, and the resultant forces that act on them. The choice of components is whatever decomposition makes sense for a specific system dynamics model.
Systems#
System models define the composite behavior produced by combining the component models. They calculate whatever physical rates of change are necessary to describe the system dynamics, such as translational and angular acceleration.
State variables#
State variables are numbers that summarize the current “state” of a dynamical system, such as position and velocity. The time derivatives of the state variables, called the state dynamics, describe how the state of the system is reacting to the current state and any system inputs. Flight simulation is performed by integrating the state dynamics over time to produce a state trajectory: a record of the dynamic behavior of the system over time. A state dynamics model is responsible for choosing a set of state variables and relating their derivatives to the derivatives generated by the system dynamics.
At first glance the system dynamics and state dynamics can seem equivalent, but differentiating the two adds significant freedom to system model design because it separates the system dynamics from the representation of system state. For example, the state dynamics may record orientation using Euler angles, quaternions, or some other encoding; the system dynamics should not depend on the choice of encoding. Similarly, the system dynamics should not depend on position, nor should they depend on the choice of global coordinate system; the system models are free to define all quantities in local, body-fixed coordinate systems, and let the state dynamics choose representations that suit the simulation applications.
Also, the state dynamics provide the interface between the system dynamics and the simulator. Although the models included with this library are designed for use with the (rudimentary) bundled simulator, alternative state dynamics classes could — in theory — expose the same system models to more comprehensive flight simulators such as FlightGear.