To calculate the elastic stability of overall stiffened structure of missile shell under axial compression, the paper presentes a practical finite element model, so that the very nonlinear problems are linearized and the stability calculation of the overall structure is greatly simplified.

The nonlinear equation of aircraft is linearized by state transforming differential relationship between input and a new input, and the nonlinear system is decoupled to a one order linear system and a two order linear system.

Then, the nonlinear equation of motion(EOM) is linearized on the condition of little perturbation, and divided into longitudinal and lateral equations.

Establish the system model of mixed H_2/H_∞ control problem after linearize the nonlinear motion control system of aircraft,design a H_2/H_∞ robust control,and make aircraft motion system not only has stability robustness,but also satisfy some performance constrains.

Implicit difference formulation for calculating unsteady temperature field of the thrust chamber with radiation cooling for liquid rocket engine has been producted, and linearize treatment is accomplished.

The nonlinear equation of aircraft is linearized by state transforming differential relationship between input and a new input, and the nonlinear system is decoupled to a one order linear system and a two order linear system.

Then, the nonlinear equation of motion(EOM) is linearized on the condition of little perturbation, and divided into longitudinal and lateral equations.

The back section mechanical system (from the input of the reversible hydraulic servo actuating system to the rudder) is linearized, and the order is reduced to the fourth-order and the first-order.

After analyzing the parameter uncertainty and space environmental disturbances, attitude dynamics model of microsatellite are obtained accordingly, then the model is linearized.

To modeling the nonlinear part, nonlinear PWM process is linearized by equivalent-area method, so linear models of whole system in every condition are built.

Reductive group actions on affine quadrics with 1-dimensional quotient: Linearization when a linear model exists

The proof of the above results is based on a shooting technique, together with a linearization method and a scaling argument.

In the book (Adaptive Identification, Prediction and Control-Multi Level Recursive Approach), the concept of dynamical linearization of nonlinear systems has been presented.

This dynamical linearization is formal only, not a real linearization.

From the linearization procedure, we can find a new approach of system identification, which is on-line real-time modeling and real-time feedback control correction.

Linearized oscillations of delay differential equations and applications

A linearized technique is introduced in order to obtain the error estimates of the approximate solutions.

Cauchy problem for linearized system of two-dimensional isentropic flow with axisymmetrical initial data in gas dynamics

The explicit solution to Cauchy problem for linearized system of two-dimensional isentropic flow with axisymmetrical initial data in gas dynamics is given.

The trust region subproblem of our method is to minimize a conic function subject to the linearized constraints and trust region bound.

The method begins with a suitable initial guess value of the solution, then finds a suitable matrix to linearize the system and constructs an iteration algorithm to generate the monotone sequence.

The control strategies utilized real-time state variables obtained by PMU to linearize the state equations of the system, and then the linear optimal control strategy was used to design excitation controllers.

The use of SPO allows to input/output linearize and decouple the strongly coupled nonlinear robot manipulator system merely by the feedback of joint angles.

A mathematical description of the experimental curve shape has been proposed to linearize the kinetic data and estimate the rate constant for such non-enzymatic interaction.

The amplitude of the oscillations of the vibrator and the perturbations of the flow parameters corresponding to it are assumed to be small, and this makes it possible to linearize these equations.

The balance equation of surfactant amount in the vicinity of the final equilibrium state of a materially isolated solution is linearized.

The basic equation is linearized by means of a Kirchhoff type ansatz.

The equation is linearized under the assumption that the Rossby number is small.

The equations of thermal convection in a rotating plane horizontal layer of nonequilibrium turbulent fluid are obtained, the system of equations is linearized and the boundary value problem is formulated.

The problem is linearized for one-dimensional perturbations in a gas at rest.

The three-dimensional unsteady second-order non-homogeneous differential equation has been derived by superposition of a small disturbance on a given steady three-dimensional flow. Based on the assumption of high Mach numbers this second-order equation for unsteady flow reduces to a form analogous to that for steady flow. This makes it possible to solve the equation by methods used in the second-order theory for steady flows. In the course of solution the flows are constrained and corrected according to the...

The three-dimensional unsteady second-order non-homogeneous differential equation has been derived by superposition of a small disturbance on a given steady three-dimensional flow. Based on the assumption of high Mach numbers this second-order equation for unsteady flow reduces to a form analogous to that for steady flow. This makes it possible to solve the equation by methods used in the second-order theory for steady flows. In the course of solution the flows are constrained and corrected according to the PLK method, and singularities are thus eliminated. The crucial point in this procedure is to find the correct particular solutions. Two particular solutions are used. One is the approximate three-dimensional particular solution. The other is obtained under the assumption of local two-dimensionality. In addition, the uniform particular solution is given, from which the uniform second-order solutions may be obtained. Then, we have treated the unsteady problem for delta wings with low aspect ratio and supersonic leading edges. The Mach number range for application of the present theory is from supersonic to low hypersonic values with reduced frequencies up to near unity. The theoretical results derived in this work can be used to calculate the unsteady aerodynamic characteristics of wings having arbitrary airfoil sections.As experimental information for similar conditions is not yet available, we can only compare our results with those of Liu D. D. . For this reason, only the derivation for a flat delta wing oscillating at low frequencies has been carried out and an analytical expression is obtained for the first order expansion of the unsteady velocity potential. In the range of Mach numbers 4 to 8, our results are in agreement with those of Lui D. D. .It is also shown that under conditions of three-dimensional thin wings the second-order theory is valid up to Mδ=1.0, while according to application of the second-order theory to bodies of revolution by Van Dyke, the useful upper limit of M5 is only 0.7. Hence, with Mδ=0.7-1 .0, the principal non-linear effects can be calculated by our second-order theory, while for thin wings the third-order terms connected with heat transfer and entropy change can be ignored.

On the basis of the definition of Gyarmathy and Meyer for the Wilson point, the author derives a new linear equation for the droplet growth function associated with the problem of condensation of supersaturated steam in a Laval nozzle. The curve determincd by the linear equation is a better approximation to the theoretical one than those of Gyarmathy and Meyer. The author also derives a simplified equation for calculating the Wilson points and porides the computational program for this equation. The theoretical...

On the basis of the definition of Gyarmathy and Meyer for the Wilson point, the author derives a new linear equation for the droplet growth function associated with the problem of condensation of supersaturated steam in a Laval nozzle. The curve determincd by the linear equation is a better approximation to the theoretical one than those of Gyarmathy and Meyer. The author also derives a simplified equation for calculating the Wilson points and porides the computational program for this equation. The theoretical complete Wilson lines for expanding steam in a Laval nozzle with various rates of expansion have been determined. These lines are drown for a pressure from 0.1 bar to 50 bar. The rate of expansion of nozzles are 10~85~(-1), 3×10~3 S~(-1), 10~4S~(-1).

Stability is an important target of the quality of an electrical supply in an aeroplane's A.C. power system. In this paper we have presented emphatically the establsihment of the linearized mathematical model of an A.C. power system with a single generator, the program functions of calculating the stability of the power system using computer, and the calculation flow diagram. The effects of the parameters of the voltage regulaotr and the working states of the generator on the stability of the system have also...

Stability is an important target of the quality of an electrical supply in an aeroplane's A.C. power system. In this paper we have presented emphatically the establsihment of the linearized mathematical model of an A.C. power system with a single generator, the program functions of calculating the stability of the power system using computer, and the calculation flow diagram. The effects of the parameters of the voltage regulaotr and the working states of the generator on the stability of the system have also been discussed. And then the suggestions to improve further feedback compensation loop have been given.