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First, the equations of motion are transformed using the Lyapunov Floquet transformation such that the linear parts of new set of equations are time invariant.
The dynamical equations of motion are transformed using the Lyapunov Floquet (L F) transformation such that the linear parts of the resulting equations become time-invariant while the forcing and nonlinearity takes the form of quasiperiodic functions.
The equations of motion are transformed into modal space where model reduction methods are applied.
The equations of motion are transformed by using the technique of modal approximation.
Based on a single mode approximation, the partial differential equations of motion are transformed into two temporal equations.
The nonlinear partial differential equations of motion are transformed into a set of the ordinary differential equations using Galerkin's method.
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The system of three coupled equations of motion is transformed into two uncoupled equations introducing a boundary layer function.
Neglecting the membrane inertias and rotary inertias, the equation of motion is transformed into a reduced equation in the generalised transverse displacement.
The rotational motion is transformed to tendon-like behavior, which enables the location of the actuators far from the arm (e.g., on a belt around the waist).
The coupling between the motor and the cart is made by a scotch yoke mechanism, so that the motor rotational motion is transformed in horizontal cart motion over a rail.
The given equation of motion is transformed into the modal co-ordinates of the undamped system and the transformed damping matrix is decomposed into proportional and purely non-proportional terms.
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