Establish relationship between component Through variables and nodes

branches a : node1.a -> node2.a; end

`branches`

begins the branches section, which
is terminated by an `end`

keyword. This section contains
one or more branch statements, which establish the relationship between
the Through variables of the component and the domain.

For example, a domain declaration contains a Through variable `a`

:

variables(Balancing=true) a = { 0, 'N' } end

and a component declares two nodes, `node1`

and `node2`

,
associated with this domain, and a variable `a`

:

variables a = { 0, 'N' }; end

The name of the component variable does not have to match that
of the domain variable, but the units must be commensurate (in this
example, `'N'`

, `'kg*m/s^2'`

, `'lbf'`

,
and so on).

To establish a connection between the component variable `a`

and
the domain Through (balancing) variable `a`

, write
a branch statement, such as:

branches a : node1.a -> node2.a; end

`node1.a`

and `node2.a`

identify
the conserving equations on `node1`

and `node2`

,
and the component variable `a`

is a term participating
in those conserving equations. The branch statement declares that `a`

flows
from `node1`

to `node2`

. Therefore, `a`

is
subtracted from the conserving equation identified by `node1.a`

,
and `a`

is added to the conserving equation identified
by `node2.a`

.

A component can use each conserving equation identifier multiple times. For example, the component declares the following variables and branches:

variables a1 = { 0, 'N' } a2 = { 0, 'N' } a3 = { 0, 'N' } end branches a1 : node1.a -> node2.a; a2 : node1.a -> node2.a; a3 : node2.a -> node1.a; end

Then, assuming that `node1`

and `node2`

are
not referenced by any other `branch`

or `connect`

statements,
the conserving equations at these nodes are:

For

`node1`

- a1 - a2 + a3 == 0

For

`node2`

a1 + a2 - a3 == 0

The following rules apply:

Each conserving equation belongs to a node associated with a domain. All variables participating in that conserving equation must have commensurate units.

A node creates one conserving equation for each of the Through (balancing) variables in the associated domain. Branch statements do not create new equations. They add and subtract terms in the existing conserving equations at the nodes.

The second and third arguments do not need to be associated with the same domain. For example, one can be associated with a gas domain, and the other with a thermal domain, with the heat flow exchange defined by the branch statement.

You can replace either the second or the third argument with

`*`

to indicate the reference node. When you use`*`

, the variable indicated by the first argument is still added to or subtracted from the equation indicated by the other identifier, but no equation is affected by the`*`

.

If a component declaration section contains two electrical nodes, `p`

and `n`

,
and a variable `i = { 0, 'A' }; `

specifying current,
you can establish the following relationship in the `branches`

section:

branches i : p.i -> n.i; end

This statement defines current `i`

as a Through
variable flowing from node `p`

to node `n`

.

For a grounding component, which has one electrical node `V`

,
define current `i`

as a Through variable flowing
from node `V`

to the reference node:

branches i : V.i -> *; end

For a mutual inductor or transformer, with primary and secondary
windings, the `branches`

section must contain two
statements, one for each winding:

branches i1 : p1.i -> n1.i; i2 : p2.i -> n2.i; end

For a component such as a constant volume pneumatic chamber, where you need to establish the heat flow exchange between the pneumatic and the thermal domains, the declaration section contains the two nodes and the heat flow variable:

nodes A = foundation.pneumatic.pneumatic; H = foundation.thermal.thermal; end variables h = { 0 , 'J/s' }; end

and the `branches`

section establishes the
heat flow exchange between the two domains:

branches h : A.Q -> H.Q; end

This statement defines the heat flow `h`

as
a Through variable flowing from the pneumatic node `A`

,
associated with the chamber inlet, to the thermal node `H`

,
associated with the thermal mass of gas in the chamber.

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