| Figure 1‑1 Modern design process for a system or component |
1 |
| Figure 2‑1 Lagrangian surface visualized in space |
2.1 |
| Figure 2‑2 A sketch for visualizing Euler-Lagrange’s equation |
2.1 |
| Figure 2‑3 A frictionless mass-spring system |
2.2 |
| Figure 2‑4 Sketch for variation of for an arbitrary |
2.5 |
| Figure 2‑5 A mass-spring system with three degrees of freedom |
2.11 |
| Figure 2‑6 Sample results as output from 20-sim |
2.11 |
| Figure 2‑7 A mass-spring-damper system with two degrees of freedom |
2.12 |
| Figure 2‑8 Sample results as output from 20-sim |
2.12 |
| Figure 2‑9 A two-loop electrical circuit with source |
2.13 |
| Figure 2‑10 Sample results as output from 20-sim |
2.13 |
| Figure 2‑11 A compound Atwood’s machine. |
2.14 |
| Figure 2‑12 Atwood’s machine |
2.15 |
| Figure 2‑13 A complex vibrating mechanical system |
2.16 |
| Figure 2‑14 Sample results as output from 20-sim |
2.16 |
| Figure 2‑15 Pendulum with oscillating pivot |
2.17 |
| Figure 2‑16 Sample results as output from 20-sim |
2.17 |
| Figure 2‑17 A pendulum attached to a mass-spring-damper system |
2.18 |
| Figure 2‑18 Sample results as output from 20-sim |
2.18 |
| Figure 2‑19 A particle moving on a circular ring |
2.19 |
| Figure 2‑20 Sample results as output from 20-sim |
2.19 |
| Figure 2‑21 An extensible robotic arm carrying a load |
2.20 |
| Figure 3‑1 Sketch of a mechanical system with its components category types |
3.2 |
| Figure 3‑2 Bond graph power direction and associated effort and flow definitions, B receives power from A |
3.2 |
| Figure 3‑3 Causality assignment definition and directions of effort and flow between elements A and B |
3.3 |
| Figure 3‑4 Causality assignments for an I-element, with preferred integral causality indicated by dashed circle (left) and derivative causality (right) |
3.4.1 |
| Figure 3‑5 Block diagram (left) and equivalent bond graph for an I-element with assigned integral causality and state variable |
3.4.1 |
| Figure 3‑6 Block diagram (left) and equivalent bond graph for an I-element with assigned derivative causality |
3.4.1 |
| Figure 3‑7 Causality assignments for a C-element, with preferred one indicated by dashed circle, integral causality (right) and derivative causality (left) |
3.4.2 |
| Figure 3‑8 Block diagram (left) and equivalent bond graph for a C-element with assigned integral causality and state variable |
3.4.2 |
| Figure 3‑9 Block diagram (left) and equivalent bond graph for a C-element with assigned derivative causality |
3.4.2 |
| Figure 3‑10 Causality assignments for an R-element |
3.4.3 |
| Figure 3‑11 Block diagrams (left) and equivalent bond graph for an R-element with assigned causality |
3.4.3 |
| Figure 3‑12 Bond graph symbols for effort source (left) and flow source (right) with their assigned causalities |
3.4.4 |
| Figure 3‑13 Bond graph symbol for 1-junction element with four connecting bonds, corresponding causalities, and strong bond identified with thick half-arrow |
3.4.5 |
| Figure 3‑14 Bond graph symbol for 0-junction element with four connecting bonds, corresponding causalities, and strong bond identified with thick half-arrow |
3.4.5 |
| Figure 3‑15 Block diagrams (left) and equivalent bond graphs for a TF-element with related assigned causalities—inputs are shown with thick arrows |
3.4.6 |
| Figure 3‑16 Block diagrams (left) and equivalent bond graphs for a GY-element with related assigned causalities—inputs are shown with thick arrows |
3.4.6 |
| Figure 3‑17 Consistency of integral causality assignment and state variable for an I-element with parameter m |
3.5.1 |
| Figure 3‑18 Consistency of integral causality assignment and state variable for a C-element with parameter c |
3.5.1 |
| Figure 4‑1 A mass-spring-damper mechanical system |
4.3 |
| Figure 4‑2 Bond graph model for a one-DOF mass-spring-damper system |
4.3 |
| Figure 4‑3 Simplified bond graph model for a one-DOF mass-spring-damper system |
4.3 |
| Figure 4‑4 A two-DOF mass-spring-damper mechanical system |
4.4 |
| Figure 4-5 Bond graph model for a two-DOF mass-spring-damper mechanical system |
4.4 |
| Figure 4-6 A three-DOF mass-spring-damper mechanical system |
4.5 |
| Figure 4-7 Bond graph model for a three-DOF mass-spring-damper mechanical system |
4.5 |
| Figure 4-8 Kinetics of a one-DOF mechanical system with showing the stream of efforts with its bond graph model |
4.6 |
| Figure 4-9 Kinematics of a one-DOF mechanical system with showing the stream of flows with its bond graph model |
4.6 |
| Figure 4-10 Traditional approach for system simulation and design |
4.7.1 |
| Figure 4-11 Modern approach for system simulation and design |
4.7.2 |
| Figure 5‑1 The 20-sim Editor interface |
5.1 |
| Figure 5‑2 The 20-sim Simulator interface |
5.1 |
| Figure 5‑3 Process steps for design of a system using the modeling, simulation and analysis |
5.1 |
| Figure 5‑4 Sketch for a car seat mechanical system |
5.2 |
| Figure 5‑5 Bode graph model for a car seat |
5.2 |
| Figure 5‑6 Sketch for a cart system carrying a load |
5.3 |
| Figure 5‑7 Bond graph model for the cart carrying a load |
5.3 |
| Figure 6‑1 Decomposition of 2D rigid-body motion into translation and rotation |
6.3 |
| Figure 6‑2 Gear and shaft mechanical system sketch |
6.4 |
| Figure 6‑3 Bond graph model for a gear shaft system, built in 20-sim |
6.4 |
| Figure 6‑4 Bond graph model for a gear shaft system, derivative causalities removed |
6.4 |
| Figure 6‑5 A double pinion-rack mechanical system |
6.5 |
| Figure 6‑6 Bond graph model for the double pinion-rack system |
6.5 |
| Figure 6‑7 A mass-spring-damper system on an inclined plane |
6.6 |
| Figure 6‑8 Bond graph model for the mass-spring-damper system on an inclined plane |
6.6 |
| Figure 6‑9 Half-car mechanical system sketch |
6.7 |
| Figure 6‑10 Bond graph model for a half-car mechanical system |
6.7 |
| Figure 6‑11 A mass-spring-damper mechanical system attached to a lever |
6.8 |
| Figure 6‑12 A mass-spring-damper mechanical system attached to a beam |
6.9 |
| Figure 6‑13 Two moving mass-spring system attached to a lever |
6.10 |
| Figure 6‑14 A two-pulley mechanical system |
6.11 |
| Figure 7‑1 Sign convention for electrical current through passive elements, passive sign convention |
7.2 |
| Figure 7‑2 Electrical power sign for several elements according to passive sign convention |
7.2 |
| Figure 7‑3 Sketch for a RCL electrical circuit in series |
7.4 |
| Figure 7‑4 Bond graph model for a RCL electrical circuit in series |
7.4 |
| Figure 7‑5 Simplified bond graph model for a RCL electrical circuit in series |
7.4 |
| Figure 7‑6 Sketch for a RCL electrical circuit in parallel |
7.5 |
| Figure 7‑7 Bond graph model for a RCL electrical circuit in parallel |
7.5 |
| Figure 7‑8 A two-loop RCL electrical circuit |
7.6 |
| Figure 7‑9 Bond graph model for the two-loop RCL electrical circuit |
7.6 |
| Figure 7‑10 A three-loop electrical circuit |
7.7 |
| Figure 7‑11 Bond graph model for the three-loop RCL electrical circuit |
7.7 |
| Figure 7‑12 A Wheatstone bridge electrical circuit |
7.8 |
| Figure 7‑13 Bond graph model for the Wheatstone bridge circuit |
7.8 |
| Figure 7‑14 A multi-loop electrical circuit |
7.9 |
| Figure 7‑15 Bond graph model for the multi-loop electrical circuit |
7.9 |
| Figure 7‑16 A multi-loop electrical circuit with transformer |
7.10 |
| Figure 7‑17 Bond graph model for the multi-loop electric circuit with transformer |
7.10 |
| Figure 8‑1 Sketches for pressure drop in a pipe and a storage tank |
8.1 |
| Figure 8‑2 Sketch for a control volume of flowing fluid in a pipe |
8.4 |
| Figure 8‑3 Sketch of velocity profile for a Hagen-Poiseuille flow in a pipe |
8.5 |
| Figure 8‑4 Sketch for a two-tank hydraulic system |
8.8 |
| Figure 8‑5 Bond graph model for a two-tank hydraulic system |
8.8 |
| Figure 8‑6 A hydraulic system with pump |
8.10 |
| Figure 8‑7 Bond graph model for the pump-reservoir-valve hydraulic system |
8.10 |
| Figure 8‑8 A hydraulic lift system |
8.11 |
| Figure 8‑9 Bond graph model for hydraulic lift system |
8.11 |
| Figure 9‑1 A car brake hydro-mechanical system |
9.2 |
| Figure 9‑2 Bond graph model for the car brake hydro-mechanical system |
9.2 |
| Figure 9‑3 An Electro-mechanical system with load |
9.3 |
| Figure 9‑4 Bond graph model for an electro-mechanical system |
9.3 |
| Figure 9‑5 A drive shaft mechanical system carrying a torsional load |
9.4 |
| Figure 9‑6 Bond graph model for the drive shaft mechanical system carrying a torsional load |
9.4 |
| Figure 9‑7 An inverted double pendulum system |
9.5 |
| Figure 9‑8 Bond graph model for the inverted double pendulum |
9.5 |
| Figure 10‑1 Linear system sketch for processing inputs and outputs |
10.3 |
| Figure 10‑2 Linear System Editor interface in 20-sim |
10.4 |
| Figure 10‑3 Transfer Function Editor interface in 20-sim |
10.4 |
| Figure 10‑4 Bode plots for a PI controller |
10.4 |
| Figure 10‑5 Model Linearization interface in 20-sim |
10.4.1 |
| Figure 10‑6 Typical Bode plots for a system |
10.4.1 |
| Figure 10‑7 Bode plots for the transfer function |
10.5 |
| Figure 10‑8 Mechanical system sketch for Example given in section 10-6 |
10.6 |
| Figure 10‑9 Bode plots for mechanical system given in section 10-6 |
10.6 |
| Figure 11‑1 Implementing gravity force for a bond graph model, in 20-sim |
11.3 |
| Figure 11‑2 A mechanical system sketch |
11.4.1 |
| Figure 11‑3 Bond graph model for the mechanical system with labelled power bonds |
11.4.1 |
| Figure 11‑4 Bond graph model for the electrical system with labelled power bonds |
11.4.2 |
| Figure 11‑5 A bond graph model with derivative causality, colour-coded |
11.5.1 |
| Figure 11‑6 A bond graph model with algebraic loop causality |
11.5.2 |
| Figure 11‑7 The bond graph model with removed algebraic loop-selecting R3 |
11.5.2 |
| Figure 11‑8 The bond graph model with removed algebraic loop-selecting R2 |
11.5.2 |
| Figure 11‑9 The bond graph model with removed algebraic loop-selecting R1 |
11.5.2 |
