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Inertial Morphing as a Novel Concept in Attitude Control and Design of Variable Agility Acrobatic Autonomous Spacecraft

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This book chapter presents a systematic overview of the novel concept of “inertial morphing (IM)”, first introduced by the authors in 2017 and further expanded in their following publications. It involves deliberate changes of the inertial properties of the system for control of the attitude of the spacecraft.

The “inertial morphing” control concept is essentially based on the realisation that the spinning spacecraft can be seen and utilised as gyroscope itself, instead of utilisation of complex, heavy and energy-consuming gyroscopic devices on-board. Utilisation of the concept, therefore, enables reduction of the weight and dimensions of the conventional systems.

It has been discovered and demonstrated via versatile numerical simulations that IM can be used to enable spacecraft with wide range of attitude control capabilities (e.g. 90° and 180° inversions, de-tumbling and controlled agility acrobatic manoeuvrings). Moreover, it has been also discovered that control of very complex manoeuvres can be achieved with a few only controlled inertial morphing actions (two and three morphings correspondingly for 180° and 90° inversions).

The general control methods presented in this chapter are based on the geometric interpretation of the arbitrary 3D rotational motion of the spacecraft, using angular momentum sphere and kinetic energy ellipsoid in the non-dimensional coordinates. The key control strategies involve combination of installing the angular momentum vector into transition polhodes and installing into transition separatrices.

Reduction in weight and dimensions, simplicity of the implementation of the inertial morphing and simplicity of the attitude control, requiring two or three discrete control actions, make this technology attractive for a variety of applications, especially involving autonomous spacecraft.

One of the remarkable features of the IM control is the ability to access a range of solutions between agile (fast) and prolonged (slow) types and select the most appropriate speed of the undertaking attitude manoeuvre. This added variable agility may be useful, for example, to perform for autonomous spacecraft surveillance, landing or manoeuvring. In particular, the IM may foster effective protection of the spacecraft from hostile environments (asteroids, radiation, etc.), as the spacecraft would be able to quickly expose the most protective surfaces to the sources of danger, hence prolonging survivability of the system. In the other cases of capturing the tumbling spacecraft, the prolonged mode can be selected, allowing more time for the capture and handling.

For the practical implementation of the IM concept, this book chapter also presents a range of conceptual mechanical designs. As Euler’s equation for the rotational motion of the rigid bodies paved the way for the development of the theory of gyroscopes and design of various gyroscopic systems, the paradigm of “inertial morphing” may prompt development of new generation of the acrobatic spacecraft with significantly reduced weight and dimensions, reduced cost and enhanced operational capabilities. It may be also possible to design new classes of gyroscopes, possessing an added-on sense of time, which is in contrast to the classical gyroscopes that only possess a sense of orientation.

With a wide spectrum of the presented examples, related to the application of a novel design concept of “inertial morphing”, it is believed that presented concept, modelling and simulation of the spinning systems and attitude control method of the spinning systems will be useful not only for the specialists but for a very wide audience, including engineers, scientists, students and enthusiasts of science and space technology.


  • Rigid-body dynamics
  • International Space Station
  • Spacecraft dynamics
  • Polhode-to-polhode transfer
  • Attitude dynamics

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Correspondence to Pavel M. Trivailo .

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5.1.1 Nomenclature

ψ, θ, ϕ Euler angles
ω x, ω y, ω z Components of the angular velocity
ω x,i, ω y,i, ω z,i Initial components of the angular velocity
a x, a y, a z Values of the semi-major axes of the ellipsoid of the kinetic energy
α Angle between the plane of the separatrix and axis with maximum moment of inertia
β Masses position angle in the “scissors” and “rhombus” mechanisms
G Centre of the mass of the spacecraft
\( \overrightarrow{\mathbf{H}}(t) \) Angular momentum vector
\( H=\mid \overrightarrow{\mathbf{H}}\mid \) Value of the system’s angular moment
\( {\overline{H}}_x,{\overline{H}}_y,{\overline{H}}_z \) Non-dimensionalised components of the angular momentum vector
I xx, I yy, I zz Principal moments of inertia
k Parameter in complete elliptic integral k
K(k) Complete elliptic integral of the first kind
K 0 Kinetic energy of the system
l Angular momentum vector of wheels, expressed in the body-fixed reference frame
m x, m y, m z Dumbbell masses in six-mass spacecraft model
\( {n}_{\omega_i} \) Control torque applied to the i-th wheel
M Mass matrix
N x, N y, N z Torque components
P Pivot point
P, Q, R Torque components in original Euler’s work
r x, r y, r z Axial positions of the spacecraft masses in the “six-mass” model
t Time
T Period of the flipping motion
x, y, z Principal body axes of the rigid body
x Vector of system’s states

5.1.2 Acronyms/Abbreviations

ISS International Space Station
AMS Angular momentum sphere
KEE Kinetic energy ellipsoid
IM Inertial morphing

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Trivailo, P.M., Kojima, H. (2022). Inertial Morphing as a Novel Concept in Attitude Control and Design of Variable Agility Acrobatic Autonomous Spacecraft. In: Dai, L., Jazar, R.N. (eds) Nonlinear Approaches in Engineering Application. Springer, Cham.

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