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The shape derivatives are derived by using a Lagrangian function and the adjoint method.
The constraint equations and useful properties of the desired mechanism are derived by using the concept of cross-ratio.
Theoretical formulations are derived by using Hamilton's principle.
Here the results are derived by using augmented Lyapunov functionals.
Governing equations are derived by using Hamilton's principle.
The dispersive equations are derived by using Bloch theorem.
The equations of motion are derived by using Hamilton's principle.
Horizontal winds are derived by using the conventional full correlation analysis method.
Finally, the conservation laws of this equation are derived by using its linear spectral problem.
New criteria on exponential stability are derived by using the second method of Lyapunov.
Some -stability criteria are derived by using the Lyapunov-Krasovskii functional method.
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