--- title: "Bond graph" chunk: 10/11 source: "https://en.wikipedia.org/wiki/Bond_graph" category: "reference" tags: "science, encyclopedia" date_saved: "2026-05-05T14:13:40.582713+00:00" instance: "kb-cron" --- These equations can be manipulated to yield the state equations. For this example, one is trying to find equations that relate p ˙ 3 ( t ) {\textstyle {\dot {p}}_{3}(t)} and q ˙ 6 ( t ) {\textstyle {\dot {q}}_{6}(t)} in terms of p 3 ( t ) {\textstyle p_{3}(t)} , q 6 ( t ) {\textstyle q_{6}(t)} , and e 1 ( t ) {\textstyle e_{1}(t)} . To start, one should recall from the tetrahedron of state that p ˙ 3 ( t ) = e 3 ( t ) {\textstyle {\dot {p}}_{3}(t)=e_{3}(t)} starting with equation 2, one can rearrange it so that e 3 = e 1 − e 2 − e 4 {\displaystyle e_{3}=e_{1}-e_{2}-e_{4}} . e 2 {\displaystyle e_{2}} can be substituted for equation 4, while in equation 4, f 2 {\displaystyle f_{2}} can be replaced by f 3 {\displaystyle f_{3}} due to equation 3, which can then be replaced by equation 5. e 4 {\displaystyle e_{4}} can likewise be replaced using equation 7, in which e 5 {\displaystyle e_{5}} can be replaced with e 6 {\displaystyle e_{6}} which can then be replaced with equation 10. Following these substituted yields the first state equation which is shown below. p ˙ 3 ( t ) = e 3 ( t ) = e 1 ( t ) − R 2 I 3 p 3 ( t ) − r C 6 q 6 ( t ) {\displaystyle {\dot {p}}_{3}(t)=e_{3}(t)=e_{1}(t)-{\frac {R_{2}}{I_{3}}}p_{3}(t)-{\frac {r}{C_{6}}}q_{6}(t)} The second state equation can likewise be solved, by recalling that q ˙ 6 ( t ) = f 6 ( t ) {\textstyle {\dot {q}}_{6}(t)=f_{6}(t)} . The second state equation is shown below. q ˙ 6 ( t ) = f 6 ( t ) = r I 3 p 3 ( t ) − 1 R 7 ⋅ C 6 q 6 ( t ) {\displaystyle {\dot {q}}_{6}(t)=f_{6}(t)={\frac {r}{I_{3}}}p_{3}(t)-{\frac {1}{R_{7}\cdot C_{6}}}q_{6}(t)} Both equations can further be rearranged into matrix form. The result of which is below. [ p ˙ 3 ( t ) q ˙ 6 ( t ) ] = [ − R 2 I 3 − r C 6 r I 3 − 1 R 7 ⋅ C 6 ] [ p 3 ( t ) q 6 ( t ) ] + [ 1 0 ] [ e 1 ( t ) ] {\displaystyle {\begin{bmatrix}{\dot {p}}_{3}(t)\\{\dot {q}}_{6}(t)\end{bmatrix}}={\begin{bmatrix}-{\frac {R_{2}}{I_{3}}}&-{\frac {r}{C_{6}}}\\{\frac {r}{I_{3}}}&-{\frac {1}{R_{7}\cdot C_{6}}}\end{bmatrix}}{\begin{bmatrix}p_{3}(t)\\q_{6}(t)\end{bmatrix}}+{\begin{bmatrix}1\\0\end{bmatrix}}{\begin{bmatrix}e_{1}(t)\end{bmatrix}}} At this point the equations can be treated as any other state-space representation problem. == International conferences on bond graph modeling (ECMS and ICBGM) == A bibliography on bond graph modeling may be extracted from the following conferences : ECMS-2013 27th European Conference on Modelling and Simulation, May 27–30, 2013, Ålesund, Norway ECMS-2008 22nd European Conference on Modelling and Simulation, June 3–6, 2008 Nicosia, Cyprus ICBGM-2007: 8th International Conference on Bond Graph Modeling And Simulation, January 15–17, 2007, San Diego, California, U.S.A. ECMS-2006 20TH European Conference on Modelling and Simulation, May 28–31, 2006, Bonn, Germany IMAACA-2005 International Mediterranean Modeling Multiconference ICBGM-2005 International Conference on Bond Graph Modeling and Simulation, January 23–27, 2005, New Orleans, Louisiana, U.S.A. – Papers ICBGM-2003 International Conference on Bond Graph Modeling and Simulation (ICBGM'2003) January 19–23, 2003, Orlando, Florida, USA – Papers 14TH European Simulation symposium October 23–26, 2002 Dresden, Germany ESS'2001 13th European Simulation symposium, Marseilles, France October 18–20, 2001 ICBGM-2001 International Conference on Bond Graph Modeling and Simulation (ICBGM 2001), Phoenix, Arizona U.S.A. European Simulation Multi-conference 23-26 May, 2000, Gent, Belgium 11th European Simulation symposium, October 26–28, 1999 Castle, Friedrich-Alexander University, Erlangen-Nuremberg, Germany ICBGM-1999 International Conference on Bond Graph Modeling and Simulation January 17–20, 1999 San Francisco, California ESS-97 9TH European Simulation Symposium and Exhibition Simulation in Industry, Passau, Germany, October 19–22, 1997 ICBGM-1997 3rd International Conference on Bond Graph Modeling And Simulation, January 12–15, 1997, Sheraton-Crescent Hotel, Phoenix, Arizona 11th European Simulation Multiconference Istanbul, Turkey, June 1–4, 1997 ESM-1996 10th annual European Simulation Multiconference Budapest, Hungary, June 2–6, 1996 ICBGM-1995 Int. Conf. on Bond Graph Modeling and Simulation (ICBGM'95), January 15–18, 1995, Las Vegas, Nevada. == See also == 20-sim simulation software based on the bond graph theory AMESim simulation software based on the bond graph theory Hybrid bond graph Coenergy == Systems for bond graph == Many systems can be expressed in terms used in bond graph. These terms are expressed in the table below. Conventions for the table below: P {\displaystyle P} is the active power; X ^ {\displaystyle {\hat {X}}} is a matrix object; x → {\displaystyle {\vec {x}}} is a vector object; x † {\displaystyle x^{\dagger }} is the Hermitian conjugate of x; it is the complex conjugate of the transpose of x. If x is a scalar, then the Hermitian conjugate is the same as the complex conjugate; D t n {\displaystyle D_{t}^{n}} is the Euler notation for differentiation, where: D t n f ( t ) = { ∫ − ∞ t f ( s ) d s , n = − 1 f ( t ) , n = 0 ∂ n f ( t ) ∂ t n , n > 0 {\displaystyle D_{t}^{n}f(t)={\begin{cases}\displaystyle \int _{-\infty }^{t}f(s)\,ds,&n=-1\\[2pt]f(t),&n=0\\[2pt]{\dfrac {\partial ^{n}f(t)}{\partial t^{n}}},&n>0\end{cases}}} { ⟨ x ⟩ α := | x | α sgn ⁡ ( x ) ⟨ a ⟩ = k ⟨ b ⟩ β ⟹ ⟨ b ⟩ = ( 1 k ⟨ a ⟩ ) 1 / β {\displaystyle {\begin{cases}\langle x\rangle ^{\alpha }:=|x|^{\alpha }\operatorname {sgn}(x)\\\langle {a}\rangle =k\langle b\rangle ^{\beta }\implies \langle b\rangle =\left({\frac {1}{k}}\langle a\rangle \right)^{1/\beta }\end{cases}}}