Sentence examples for by linearizing the equations from inspiring English sources
The rigid-body motion and elastic deformations are decoupled by linearizing the equations of motion around the rigid-body reference trajectory.
The analysis was conducted by linearizing the equations about their equilibrium points and studying the influence of the averaged external heat loads and the periodic parts separately.
Nonlinear equations in mathematical physics and engineering are solved by linearizing the equations and forming various iterative procedures, then executing the numerical simulation.
Stability is determined by linearizing the equations of motion about a steady motion and calculating the eigenvalues using a finite difference discretization.
In this paper, JFNK method is employed to solve a class of non-equilibrium radiation diffusion coupled to material thermal conduction equations, and two preconditioners are designed by linearizing the equations in two methods.
The spinover mode is then considered, by linearizing the equation of motion for the fluid.
The linear model of AHWR, obtained by linearizing the nonlinear equations is found to be highly ill-conditioned.
Small perturbation propagation in fluid flows is usually examined by linearizing the governing equations about a steady basic state.
A conceptual framework for studying such solutions is the linear spreading velocity υ*, which is the asymptotic rate with which an initial localized perturbation spreads into an unstable state based on the linear equations obtained by linearizing the full nonlinear equations about the unstable state.
Then Eq. (1) arises naturally by linearizing the Klein Gordon equation variable boundary (see [2]): partial_{t}^{2}u-xpartial_{x ^{2}u-xpartial_{x }^{2}u+C_{ 1}, in (mathbb{C}_), which shows that u=bigl(t^{2}-4xbigr)^{frac{1}{1-partial_{x}u=au^{p}
By linearizing the process equation (12) around x k − 1 | k − 1 i, j, we have x k ≈ f ( x k − 1 | k − 1 i, j ) + F k i, j ( x k − 1 − x k − 1 | k − 1 i, j ) + u k, u k ∼ N ( 0 4 × 1, Q ), where F k i, j is the jacobian matrix of f with respect to the state F k i, j ≈ ∂f ( x k ) ∂ x k x k = x k − 1 | k − 1 i, j.
