Table 1.

List of symbols.

Symbol	Explanation
a n	Fourier series cosine coefficient
A	constant system matrix in LTI model
b n	Fourier series sine coefficient
c n	Fourier sine series coefficient
g	gravitational acceleration
h	number of harmonics in Fourier series
I yy	pitching moment of inertia about y-axis
m	body mass
M	pitching moment about y-axis
n	counting index
p	vector giving the coordinates of a point in state space
p	p-value in statistical tests
P	vector of system parameters
P(t)	periodic function
$\hat{P}(t)$	discrete periodic function
q	rotational velocity about y-axis (pitch rate)
t	vector giving tangent direction to a curve in state space
t	time
T	wing beat period
u	translational velocity component in x-direction
U	wind tunnel speed
U ref	reference tunnel speed (3.50 m s−1)
w	velocity in z-direction
x	state vector
X	vector of total forces due to locust
Xα(t)	vector function of change in instantaneous forces with α
Xref(t)	vector function of instantaneous forces in reference condition
XU(t)	vector function of change in instantaneous forces with U
X	force component in x-direction
Z	force component in z-direction
α	body angle of x-axis to oncoming flow
α ref	reference body angle (7°)
ϕ n	phase angle
Φ(t)	phase function
Φ	phase vector
θ	pitch attitude
ω	angular frequency of wing beat
Common subscripts and superscripts
$\overline{\text{e}}$	value of a system state at quasi-static equilibrium
i	counting index
n	counting index
q	partial derivative with respect to q
Ref	variable or function under reference conditions
T	vector transposition
u	partial derivative with respect to u
U	partial derivative with respect to U
w	partial derivative with respect to w
0	value of a state variable at time t=0
α	partial derivative with respect to α
overbar	quasi-static value of a term