Good day I would just like to ask if a fixed wing aircraft such as a glider(without thrust capability therefore needs external forces such as air flow to move constraining its movement) can be considered a non-holonomic system considering the fact that it cannot move freely compared to a quadcopter that is holonomic.

I found this information from: What's the difference between a holonomic and a nonholonomic system?


Holonomic system are systems for which all constraints are integrable into positional constraints.

Nonholonomic systems are systems which have constraints that are nonintegrable into positional constraints.


Holonomic system where a robot can move in any direction in the configuration space.

Nonholonomic systems are systems where the velocities (magnitude and or direction) and other derivatives of the position are constraint.


1 Answer 1


The glider definitely is a nonholomonic system, but not (only) because it has no propulsion.

As Wikipedia defines it:

A nonholonomic system in physics and mathematics is a system whose state depends on the path taken in order to achieve it.

So, if an aircraft can reach a pose (position and orientation) in space regardless of its prior states (path taken) than it is holomonic. To simplify it even more:

A car is a nonholomonic system. It can occupy any position (in 2D, X and Y translations) and orientation (1 orientation around the Z axiz, perpendicular to the road) but what makes it nonholominic is its steering system which does not allow it to move sideways. It can occupy the position just 1 mm (or $\delta y$ distance) to the right of its current position, but ONLY if an adecvate path leads the car to that position.

An omnidirectional robot (e.g. with mecanum wheels, Google search it) is holomonic because it can occupy any pose (2 translations 1 orientation) regardless of its previous states (path taken). It can move to the immediate right, unlike the car, with $\delta y$ distance.

You might want to take a look at underactuated systems. Those are the ones that require external forces.


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