Sentence examples for identically satisfied from inspiring English sources

Mass conservation and the Hamilton Jacobi equation for the potential are identically satisfied by constant mass transport along straight lines.

It is also found that this method is a generalization of the L'Hopital's Rule to the case of multi-unknowns with multi-equations, some of which are identically satisfied.

The analysis is based on an inverse vibration problem: Given a candidate mode shape and density distribution, we calculate the plate stiffness so that the governing equation for the plate mode shape is identically satisfied.

For harmonic oscillation these four partial differential equations are combined into an eighth order ordinary differential equation, which is identically satisfied by all components of bending displacements and bending rotations.

In order to overcome this problem, a limit-based approach is presented in this paper, where the limit to the cylindrical orthotropy is considered, and by using the Taylor series of expansion, the equations replacing the identically satisfied ones are derived.

The continuity equation is identically satisfied.

Next, the elasticity problem for the simply supported plate for each instantaneous temperature distribution is analyzed by using displacement functions that identically satisfy boundary conditions at the edges.

Displacement functions that identically satisfy boundary conditions are used to reduce the governing equations to a set of coupled ordinary differential equations with variable coefficients.

Suitable temperature and displacement functions that identically satisfy the simply supported boundary conditions are used to reduce the thermoelastic equilibrium equations to a set of coupled ordinary differential equations with variable coefficients, which can be solved by differential quadrature method.

Rayleigh Ritz variational method is applied to the determination of the first four frequency coefficients for the title problem by making use of coordinate functions which identically satisfy the boundary conditions at the outer edge.

The governing partial differential equations are reduced to ordinary differential equations in the thickness coordinate by expanding all entities for each layer in double Fourier series in span coordinates, which identically satisfy the boundary conditions at the simply-supported ends.