Mode of access: World Wide Web.

System requirements: Adobe Acrobat Reader.

Part of: Synthesis digital library of engineering and computer science.

Includes bibliographical references (pages 193-194).

Preface -- Language of mathematics -- The language of experts -- The importance of triangulation -- The captains of energy story -- Outline of book -- Acknowledgments --

1. If you push it, it will flow -- 1.1 The effort-flow analogy -- 1.1.1 System elements -- 1.1.2 The energy balance principle --

2. Governing dynamics -- 2.1 Deriving a governing differential equation -- 2.2 The four casts -- 2.3 System order -- 2.4 Linearity --

3. The electrical cast -- 3.1 Effort and flow variables -- 3.2 Storage elements -- 3.2.1 Potential energy storage character -- 3.2.2 Kinetic energy storage character -- 3.3 Dissipative elements -- 3.4 Single storage element scripts -- 3.4.1 RC circuits -- 3.4.2 RL circuits -- 3.4.3 A generalized mathematical form for the single storage element script -- 3.5 Multiple storage element scripts -- 3.5.1 Series RLC circuits -- 3.5.2 Parallel RLC circuits -- 3.5.3 Idealized LC circuits -- 3.5.4 A generalized mathematical form for the dual storage element script -- 3.6 Chapter activities --

4. The mechanical cast -- 4.1 Effort and flow variables -- 4.2 Storage elements -- 4.2.1 Potential energy storage character -- 4.2.2 Kinetic energy storage character -- 4.3 Dissipative elements -- 4.4 Single storage element scripts -- 4.4.1 Spring-damper systems -- 4.4.2 Mass-damper systems -- 4.4.3 A generalized mathematical form for the single storage element script -- 4.5 Multiple storage element scripts -- 4.5.1 The classical mass-spring-damper system -- 4.5.2 Idealized mass-spring systems -- 4.5.3 A generalized mathematical form for the dual storage element script -- 4.6 Rotational mechanical systems -- 4.6.1 Effort and flow variables -- 4.6.2 Storage elements -- 4.6.3 Dissipative elements -- 4.6.4 The simple pendulum -- 4.7 Chapter activities --

5. A common notion -- 5.1 Time domain solutions of 1st order systems -- 5.1.1 Transient response -- 5.1.2 Forced response -- 5.1.3 Dimensionless solutions for 1st order systems -- 5.1.4 Universal truths for 1st order system response in the time domain -- 5.2 Time domain solutions of 2nd order systems -- 5.2.1 Free response -- 5.2.2 Forced response -- 5.2.3 Dimensionless solutions for 2nd order systems -- 5.2.4 Characteristic times for transients in 2nd order systems -- 5.2.5 Universal truths for 2nd order system response in the time domain -- 5.2.6 Energy storage and dissipation for 2nd order system response in the time domain -- 5.3 Chapter activities --

6. Going nowhere? -- 6.1 Frequency domain solutions of 1st order systems -- 6.1.1 Transfer function analysis for harmonic input -- 6.1.2 Steady-state response and Bode plot analysis -- 6.1.3 An interpretation of dimensionless frequency ratio -- 6.1.4 Filtering characteristics of 1st order systems -- 6.1.5 Universal truths for 1st order systems subject to harmonic input -- 6.1.6 Energy storage and dissipation in 1st order systems subject to harmonic input excitation -- 6.2 Frequency domain solutions of 2nd order systems -- 6.2.1 Transfer function analysis for harmonic input -- 6.2.2 Steady-state response and bode plot analysis -- 6.2.3 Universal truths for 2nd order systems subject to harmonic input -- 6.3 Redesigning systems for steady-state behaviors -- 6.4 Energy storage and dissipation in 2nd order systems subject to harmonic input excitation -- 6.5 Chapter activities --

7. The fluid and thermal casts -- 7.1 Fluid systems -- 7.1.1 Fluid effort and flow variables -- 7.1.2 Storage elements -- 7.1.3 Dissipative elements -- 7.1.4 Single storage element scripts -- 7.1.5 Multiple storage element scripts -- 7.2 Thermal systems -- 7.2.1 Thermal effort and flow variables -- 7.2.2 Storage elements -- 7.2.3 Dissipative elements -- 7.2.4 Single storage element scripts -- 7.3 Chapter activities --

8. Summary -- Afterword -- Bibliography -- Authors' biographies.

Abstract freely available; full-text restricted to subscribers or individual document purchasers.

Compendex

INSPEC

Google scholar

Google book search

In teaching an introduction to transport or systems dynamics modeling at the undergraduate level, it is possible to lose pedagogical traction in a sea of abstract mathematics. What the mathematical modeling of time-dependent system behavior offers is a venue in which students can be taught that physical analogies exist between what they likely perceive as distinct areas of study in the physical sciences. We introduce a storyline whose characters are superheroes that store and dissipate energy in dynamic systems. Introducing students to the overarching conservation laws helps develop the analogy that ties the different disciplines together under a common umbrella of system energy. In this book, we use the superhero cast to present the effort-flow analogy and its relationship to the conservation principles of mass, momentum, energy, and electrical charge. We use a superhero movie script common to mechanical, electrical, fluid, and thermal engineering systems to illustrate how to apply the analogy to arrive at governing differential equations describing the systems' behavior in time. Ultimately, we show how only two types of differential equation, and therefore, two types of system response are possible. This novel approach of storytelling and a movie script is used to help make the mathematics of lumped system modeling more approachable for students.

Also available in print.

Title from PDF title page (viewed on February 22, 2015).