Lyapunov functions from auxiliary exact differential equations
Use of auxiliary differential equations derived from nonlinear differential equations to find Lyapunov function
DIFFERENTIAL EQUATION↗
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Results for “Nonlinear equations”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
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Rational approximations to the generalized Duffing equation.
Rational approximation of generalized Duffing equation, damped mass spring oscillator equation and generalized second order Riccati equation
FORCED VIBRATION↗
A modified Newton's method for solving trajectory optimization problems.
Modified Newton method for solution of simultaneous nonlinear equations applied to variational two point boundary value problems in trajectory optimization
Lastman, G. J.↗
A parametric study of blade-motion stability boundaries for an articulated rotor
Numerical solution of coupled, nonlinear, equation of motion for rigid blade to simulate response sensitivity and blade-motion stability of fully articulated rotor
Jenkins, J. L., Jr.↗
Applications of alternating direction methods to mildly nonlinear problems
Alternating direction methods for solving mildly nonlinear equations, and iterative techniques for approximating solution
Caspar, J. R.↗
Calculation of complex chemical equilibria.
Complex chemical equilibrium calculation, analyzing thermodynamic principles and solution to nonlinear equations
Gordon, S.↗
Local mapping relations and global implicit function theorems
Nonlinear equation solution based on local mapping relations and global implicit function theorems for Banach space problems
Rheinboldt, W. C.↗
Identification of a nonlinear system using a combined algorithm
Parameter identification algorithm for nonlinear equations describing VTOL aircraft longitudinal response
Denery, D. G.↗
On the determination of near body orbits using mass concentration models
Mathematical model for near-body orbit calculation using mass concentration, perturbation theory, nonlinear equations, geopotentials, and least squares method
Childs, B.↗
Distributions of nighttime F-region molecular ion concentrations and 6300-A nightglow morphology
Nighttime F region molecular ion concentrations of oxygen and nobelium and associated nightglow morphology, using numerical method for solving nonlinear equations
Brasher, W. E.↗
Equilibrium feedback control in linear games with quadratic costs
Equilibrium strategies for linear games with quadratic costs in Hilbert space, deriving nonlinear equation in allowed operator feedback spaces
Lukes, D. L.↗
Nonlinear response of gas-lubricated shrouded Rayleigh-step thrust pad
Quasi-static pressure characteristics of gas lubricated thrust bearing with shrouded Rayleigh step pads, solving nonlinear equation of motion
Cheng, C.↗
Finite stretching of a circular plate of neo-Hookean material.
The analytical solution presented is based on the assumption that the deformed thickness of the plate is approximately constant. The nonlinear equations governing finite axisymmetric deformations of a circular plate made of neo-Hookean material are used in the analysis. The variation of circumferential extension ratio and the variation of deformed thickness are shown in graphs.
Biricikoglu, V.↗
A variable-step-size robust delta modulator.
Description of an analytically obtained optimum adaptive delta modulator-demodulator configuration. The device utilizes two past samples to obtain a step size which minimizes the mean square error for a Markov-Gaussian source. The optimum system is compared, using computer simulations, with a linear delta modulator and an enhanced Abate delta modulator. In addition, the performance is compared to the rate distortion bound for a Markov source. It is shown that the optimum delta modulator is neither quantization nor slope-overload limited. The highly nonlinear equations obtained for the optimum transmitter and receiver are approximated by piecewise-linear equations in order to obtain system equations which can be transformed into hardware. The derivation of the experimental system is presented.
Song, C. L.↗
Nonlinear instability of a helicopter blade.
The nonlinear equations of flap-lag coupled with oscillation of a torsionally rigid blade are derived. The solution is established by a simplified asymptotic expansion procedure of multiple time scales. The region of stability and limit cycle oscillation and its comparison with numerical results are presented.
Tong, P.↗
Analytic prediction of airplane equilibrium spin characteristics
The nonlinear equations of motion are solved algebraically for conditions for which an airplane is in an equilibrium spin. Constrained minimization techniques are employed in obtaining the solution. Linear characteristics of the airplane about the equilibrium points are also presented and their significance in identifying the stability characteristics of the equilibrium points is discussed. Computer time requirements are small making the method appear potentially applicable in airplane design. Results are obtained for several configurations and are compared with other analytic-numerical methods employed in spin prediction. Correlation with experimental results is discussed for one configuration for which a rather extensive data base was available. A need is indicated for higher Reynolds number data taken under conditions which more accurately simulate a spin.
Adams, W. M., Jr.↗
Optimal trajectory generation for mechanical arms
A general method of generating optimal trajectories between an initial and a final position of an n degree of freedom manipulator arm with nonlinear equations of motion is proposed. The method is based on the assumption that the time history of each of the coordinates can be expanded in a series of simple time functions. By searching over the coefficients of the terms in the expansion, trajectories which minimize the value of a given cost function can be obtained. The method has been applied to a planar three degree of freedom arm.
Iemenschot, J. A.↗
Pole and zero placement in multivariable control systems
A method is proposed for designing multivariable systems based on an alternate derivation of Davison's theorem on pole placement and the solution of the nonlinear equations for the feedback gains by the least square error method. Output feedback is used to control a complex dynamical system. The freedom in design, after allocating poles, is used to place zeros and/or satisfy other design objectives. This method results in algorithms which are computationally attractive. However, this is done at a considerable sacrifice in terms of the design freedom available. For a system with m inputs and p outputs only m + p variables are available instead of mp variables.
Sridhar, B.↗