163 Result(s)
within
Chapter
Albert C.J. Luo
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Chapter
Introduction
In this chapter, a brief history of spring-pendulum study and application will be presented, and the significance and application of the nonlinear spring-pendulum are presented. To obtain periodic motions in t...
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Chapter
A Nonlinear Spring-Pendulum
In this chapter, the physical problem of a periodically forced spring-pendulum will be presented. The implicit discrete map** structures of periodic motions will be developed, and eigenvalue analysis will be...
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Chapter
A Semi-analytical Method
In this chapter, periodic motions in dynamical systems will be presented for a review of methodology. If a nonlinear system has a periodic motion with a period of ...
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Chapter
Formulation for Periodic Motions
In this chapter, periodic motions in the nonlinear spring-pendulum will be constructed through the map** structures and the corresponding stability and bifurcation of periodic motions will be discussed. From...
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Chapter
Single-Variable Quadratic Systems with a Self-Univariate Quadratic Vector Field
In this chapter, two-dimensional single-variable quadratic systems with a self-univariate quadratic vector field are discussed, and the appearing and switching bifurcations for the 1-dimensional flows (e.g., s...
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Chapter
Variable-Independent Quadratic Dynamics
In this chapter, nonlinear dynamics of dynamical systems possessing two variable-independent univariate vector fields is discussed. The dynamical systems with a constant vector field and a variable-independent...
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Chapter
Period-1 Motions to Chaos
In this chapter, bifurcation trees of period-1 to period-2 motions in a nonlinear spring pendulum system are obtained semi-analytically. The corresponding harmonic frequency-amplitude characteristics of period...
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Chapter
Two-Univariate Product Quadratic Systems
In this chapter, nonlinear dynamics of dynamical systems possessing bivariate quadratic vector fields is discussed as in Luo (Journal of Vibration Testing and System Dynamics in 2023). The bivariate quadratic vec...
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Chapter
Product-Bivariate Quadratic Systems with a Non-Self-Univariate Quadratic Vector Field
In this chapter, nonlinear dynamics of dynamical systems possessing a bivariate product quadratic vector field and a non-self-univariate quadratic vector field is discussed as in Luo (J Vib Test Syst Dyn, 2023). ...
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Chapter
Two-Dimensional Linear Dynamical Systems
In this Chapter, two-dimensional dynamical systems with constant and linear vector fields are discussed. Dynamical systems with one-variable vector fields are presented and the singular dynamics of two-dimensi...
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Chapter
Single-Variable Quadratic Systems with a Non-Self-Univariate Quadratic Vector Field
In this chapter, two-dimensional, single-variable quadratic systems with a non-self-univariate quadratic vector fields are discussed, and the appearing and switching bifurcations for the 1-dimensional flows (e...
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Chapter
Variable-Crossing Univariate Quadratic Systems
In this chapter, nonlinear dynamics of dynamical systems with two variable-crossing univariate vector fields is discussed. The dynamical systems with a constant vector field and a variable-crossing univariate ...
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Chapter
Higher-Order Periodic Motions to Chaos
In this chapter, higher-order periodic motions to chaos will be discussed through the complete bifurcation dynamics of period-3 motions to chaos. The analytical bifurcation trees of period-3 motions to chaos a...
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Chapter
Product-Bivariate Quadratic Systems with a Self-Univariate Quadratic Vector Field
In this chapter, nonlinear dynamics of dynamical systems possessing a bivariate product vector field and a self-univariate quadratic vector field is discussed as in Luo (J Vib Test Syst Dyn, 2023). The stability ...
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Chapter
Introduction
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Chapter
Discretization
In this chapter, a physical model of the tuned mass damper system will be presented. The discrete map** will be developed for periodic motions, and period-1 and period-m motions will be discussed and the cor...
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Chapter
Independent Period-12 Motions
Semi-analytical solutions, frequency-amplitude characteristics, and simulation results of one branch period-12 motions in the frequency range of $$\Om...
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Chapter
A Semi-analytical Method
Periodic motions in nonlinear dynamical systems will be obtained through the implicit map**s obtained from the nonlinear differential equations. If a nonlinear system has a periodic motion with a period of ...
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Chapter
Independent Period-9 Motions
Semi-analytical solutions, frequency-amplitude characteristics, and simulation results of one branch period-9 motions in the frequency range of $$\Ome...
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Chapter
On Complex Periodic Evolutions of a Periodically Diffused Brusselator
Complex periodic evolutions in a periodically Diffused Brusselator are presented through the generalized harmonic balance method, and the corresponding stability and bifurcations of the periodic evolutions are...
