Energy considerations

Biohydrodynamics Toolbox    

bht_energy

Compute the balance of energy, the torques of the articulations and the power expended by the articulated bodies.

Syntax

[T,E_tot,E_fl,E_fi] = bht_energy('DataFilename',filename)

[...,E_pot,E_def,E_net,torques,power] = bht_energy(...)

[...] = bht_energy(...,options)

Description

The function loads data from the MAT-File filename_results (generated by the function bht_traject_compute from the DAT-File filename) and returns:

• T: a linearly spaced vector of the time steps.
• E_tot: the total kinetic energy of the fluid-bodies system (a column vector, each row corresponding to one time step).
• E_fl: the kinetic energy of the fluid (same format as E_tot).
• E_fi: the total kinetic energy of the bodies (same format as E_tot).

When all of the solids making up the bodies are not neutrally buoyant, the function also returns:

• E_pot: the potential energy of the system fluid-bodies (same format as above) related to the buoyant force,

and when all of the bodies are not reduced to single solids:

• E_def: the kinetic energy of bodies' inner deformations i.e. due to the relative motion of the links in the body's frame (same format as E_tot).
• E_net: the bodies' kinetic energy of rigid (or global) motion (same format as above). The bodies' velocity can be decomposed into the velocity of deformations (due to the relative displacement of the links and expressed in the local moving frame) and the rigid velocity which is the motion of the bodies, considered as rigid, expressed in the fixed reference frame. This decomposition allows to decompose the total kinetic energy of the bodies into the rigid kinetic energy and the kinetic energy of deformations.  In particular, we always have E_fi = E_net + E_def.
• torques: the torques  of the articulations (an array of size numbers_of_time_step x numbers_of_controls).
• power: the power expended by the bodies at the joints (same format as torques) obtained by multiplying the torques by the angular velocities.

Function's options

The options are described in the following table:

option	Expected value	Default value	Description
NoComputations	on or off	off	Switch this option to 'on'  if the computations have already be done and the results saved on disk. The file 'filename_energetic_results.mat' is loaded and used to plot the graphs.
TimeRange	array [Tmin Tmax]	Time range of the DAT-File	Time interval over which the computations are done.
DrawGraph	on or off	on	Whether energy balances and power expended by the bodies are ploted at the end of the computations.
latex	on or off	off	Use latex interpreter for graphs.
SaveResults	on or off	on	Whether the results are saved in the MAT-File  filename_energy_results at the end of the computations.

Example

The statement :

[T,E_tot,E_fl,E_fi,E_pot,E_def,E_net,torques,power] = bht_energy('DataFilename',filename,'TimeRange',[50 55],'DrawGraph','no','SaveResults','off')

will return the values T,E_tot,E_fl,E_fi,E_pot,E_def,E_net,torques and power related to the experiment described in the DAT-File filename, over the time interval [50 55]. No graph will be displayed and the results will not be saved on disk.

Displayed figure overview

When the option 'DrawGraph' is set to on, a figure similar to the following one is displayed:

See also

bht_traject_compute

Seeking optimal strokes

2008 - A. Munnier and B. Pincon (Insitut Elie Cartan and INRIA Lorraine, Projet CORIDA, Nancy, France).