page_title: Bond graph
section_title: Tetrahedron of state
hierarchical_section_title: Bond graph / Tetrahedron of state
caption_attribution_description: English: An image of the Tetrahedron of State. This shows the mathematical conversions of different variables. It is commonly used with Bond Graphs.
context_page_description: A bond graph is a graphical representation of a physical dynamic system. It allows the conversion of the system into a state-space representation. It is similar to a block diagram or signal-flow graph, with the major difference that the arcs in bond graphs represent bi-directional exchange of physical energy, while those in block diagrams and signal-flow graphs represent uni-directional flow of information. Bond graphs are multi-energy domain and domain neutral. This means a bond graph can incorporate multiple domains seamlessly.
  The bond graph is composed of the "bonds" which link together "single port", "double-port" and "multi-port" elements. Each bond represents the instantaneous flow of energy or power. The flow in each bond is denoted by a pair of variables called power variables, whose product is the instantaneous power of the bond. The power variables are broken into two parts: flow and effort. For example, for the bond of an electrical system, the flow is the current, while the effort is the voltage. By multiplying current and voltage in this example you can get the instantaneous power of the bond.
context_section_description: The tetrahedron of state is a tetrahedron that graphically shows the conversion between effort and flow. The adjacent image shows the tetrahedron in its generalized form. The tetrahedron can be modified depending on the energy domain. The table below shows the variables and constants of the tetrahedron of state in common energy domains.
  Using the tetrahedron of state, one can find a mathematical relationship between any variables on the tetrahedron. This is done by following the arrows around the diagram and multiplying any constants along the way. For example, if you wanted to find the relationship between generalized flow and generalized displacement, you would start at the f(t) and then integrate it to get q(t). More examples of equations can be seen below.
  Relationship between generalized displacement and generalized flow.
  Relationship between generalized flow and generalized effort.
  Relationship between generalized flow and generalized momentum.
  Relationship between generalized momentum and generalized effort.
  Relationship between generalized flow and generalized effort, involving the constant C.
  All of the mathematical relationships remain the same when switching energy domains, only the symbols change. This can be seen with the following examples.
  Relationship between displacement and velocity.
  Relationship between current and voltage, this is also known as Ohm's law.
  Relationship between force and displacement, also known as Hooke's law. The negative sign is dropped in this equation because the sign is factored into the way the arrow is pointing in the bond graph.
caption: Tetrahedron of state
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