The dynamics of passenger aircraft on the ground are influenced by the nonlinear characteristics of several components, including geometric nonlinearities, aerodynamics, and interactions at the tire-ground interface. We present a fully parameterized mathematical model of a typical passenger aircraft that includes all relevant nonlinear effects. The full equations of motion are derived from first principles in terms of forces and moments acting on a rigid airframe, and they include implementations of the local models of individual components. The overall model has been developed from and validated against an existing industry-tested SIMMECHANICS model. The key advantage of the mathematical model is that it allows for comprehensive studies of solutions and their stability with methods from dynamical systems theory, particularly, the powerful tool of numerical continuation. As a concrete example, we present a bifurcation study of how fixed-radius turning solutions depend on the aircraft’s steering angle and center of gravity position. These results are represented in a compact form as surfaces of solutions, on which we identify regions of stable turning and regions of laterally unstable solutions. The boundaries between these regions are computed directly, and they allow us to determine ranges of parameter values for safe operation. The robustness of these results under the variation in additional parameters, specifically, the engine thrust and aircraft mass, are investigated. Qualitative changes in the structure of the solutions are identified and explained in detail. Overall our results give a complete description of the possible turning dynamics of the aircraft in dependence on four parameters of operational relevance.

1.
Klyde
,
D.
,
Myers
,
T.
,
Magdaleno
,
R.
, and
Reinsberg
,
J.
, 2002, “
Identification of the Dominant Ground Handling Charactersitics of a Navy Jet Trainer
,”
J. Guid. Control Dyn.
0731-5090,
25
(
3
), pp.
546
552
.
2.
Klyde
,
D.
,
Myers
,
T.
,
Magdaleno
,
R.
, and
Reinsberg
,
J.
, 2001, “
Development and Evaluation of Aircraft Ground Handling Maneuvers and Metrics
,”
Proceedings of the AIAA Atmospheric Flight Mechanics Conference
, Paper No. AIAA-2001-4011.
3.
Thompson
,
J.
, and
Macmillen
,
F.
, 1998, “
Nonlinear Flight Dynamics of High-Performance Aircraft
,”
Phil. Trans. R. Soc. London, Ser. A
0962-8428,
356
(
1745
), pp.
2165
2333
.
4.
Khapane
,
D. P.
, 2003, “
Simulation of Asymmetric Landing and Typical Ground Maneuvers for Large Transport Aircraft
,”
Aerosp. Sci. Technol.
1270-9638,
7
(
8
), pp.
611
619
.
5.
Doedel
,
E.
,
Champneys
,
A.
,
Fairgrieve
,
T.
,
Kuznetsov
,
Y.
,
Sandstede
,
B.
, and
Wang
,
X.
, 2001, “
AUTO 97: Continuation and Bifurcation Software for Ordinary Differential Equations
,” http://indy.cs.concordia.ca/auto/http://indy.cs.concordia.ca/auto/
6.
Krauskopf
,
B.
,
Osinga
,
H. M.
, and
Galán-Vioque
,
J.
, 2007,
Numerical Continuation Methods for Dynamical Systems
,
Springer
,
New York
.
7.
Venn
,
D.
, and
Lowenberg
,
M.
, 2004, “
Nonlinear Vehicle Dynamics Using Bifurcation Methods
,”
Proceedings of the Motorsports Engineering Conference and Exhibition
.
8.
Charles
,
G.
,
Lowenberg
,
M.
,
Stoten
,
D.
,
Wang
,
X.
, and
di Bernardo
,
M.
, 2002, “
Aircraft Flight Dynamics Analysis and Controller Design Using Bifurcation Tailoring
,”
Proceedings of the AIAA Guidance Navigation and Control Conference
, Paper No. AIAA-2002-4751.
9.
Bedford
,
R.
, and
Lowenberg
,
M.
, 2004, “
Bifurcation Analysis of Rotorcraft Dynamics With an Underslung Load
,”
Proceedings of the AIAA Atmospheric Flight Mechanics Conference
, Paper No. AIAA-2004-4947.
10.
Rankin
,
J.
,
Coetzee
,
E.
,
Krauskopf
,
B.
, and
Lowenberg
,
M.
, 2009, “
Bifurcation and Stability Analysis of Aircraft Turning on the Ground
,”
J. Guid. Control Dyn.
0731-5090,
32
(
2
), pp.
500
511
.
11.
Blundell
,
M.
, and
Harty
,
D.
, 2004,
The Multibody Systems Approach to Vehicle Dynamics
,
SAE
,
Warrendale, PA
.
12.
MathWorks
, 2004, “
Model and Simulate Mechanical Systems With SIMMECHANICS
,” http://www.mathworks.com/products/simmechanics/http://www.mathworks.com/products/simmechanics/
13.
Strogatz
,
S. H.
, 2000,
Nonlinear Dynamics and Chaos
,
Springer
,
New York
.
14.
Etkin
,
B.
, 1972,
Dynamics of Atmospheric Flight
,
Wiley
,
New York
.
15.
Phillips
,
W. F.
, 2004,
Mechanics of Flight
,
Wiley
,
New York
.
16.
Jeanneau
,
M.
, 2004, “
Description of Aircraft Ground Dynamics
,”
GARTEUR FM AG17
, Paper No. RP0412731.
17.
Pacejka
,
H. B.
, 2006,
Tyre and Vehicle Dynamics
,
Elsevier
,
New York
.
18.
Stépán
,
G.
, 1998, “
Delay, Oscillations and Shimmying Wheels
,”
Proceedings of Symposium CHAOS97
,
Kluwer
,
Dordrecht
, pp.
373
386
.
19.
Takacs
,
D.
, and
Stépán
,
G.
, 2009, “
Experiments on Quasiperiodic Wheel Shimmy
,”
ASME J. Comput. Nonlinear Dyn.
1555-1423,
4
, p.
031007
.
20.
Wong
,
J.
, 2001,
Theory of Ground Vehicles
,
3rd ed.
,
Wiley-Interscience
,
New York
.
21.
Mitchell
,
D.
, 1985, “
Calculation of Ground Performance in Take-Off and Landing
,” ESDU Data Sheet No. 85029.
22.
Kuznetsov
,
Y. A.
, 1998,
Elements of Applied Bifurcation Theory, Applied Mathematical Sciences
,
Springer-Verlag
,
New York
, Vol.
112
.
23.
Guckenheimer
,
J.
, and
Holmes
,
P.
, 1983,
Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields, Applied Mathematical Sciences
,
Springer
,
New York
, Vol.
42
.
You do not currently have access to this content.