Mathematical Modelling of Measures in BharathaNatyam

Cortez Deacetis

Mathematical Modelling involves generating a design of a actual environment system working with methods in Mathematics these kinds of as Linear Programming, Differential Equations etcetera. When the procedure product has inherent uncertainty, simulation is used in addition to the Mathematical Design to depict both a stationary or a dynamic method (Technique in Motion).

Adavus in BharathaNatyam (Classical dance art type of south India) symbolize a established of methods which do not involve expression (nrityam). So Adavus can be researched working with Mathematical Versions.

Tattu Adavu involves lifting the ft up and down so that a person can hear the tapping sound.

The “sollukattu”(tamil phrase translated into English as Verbal pronunciation of beats) is rendered in varying tempos. There are also recurring movement of the feet in a variety of counts these kinds of as 4,6 and 8.

The four verbal beats can be pronounced as tai,ya, tai,hello. If the 4 verbal beats arise at T(1), T(2), T(3) and T(4) the place T(I) is the ith quick of time when the verbal beat is pronounced by the accompanying artiste.

The pace or the tempo is given by T(2) – T(1) T(3) – T(2) and T(4) – T(3). Ideally all these time intervals must be equal. It can be equivalent if these beats are device generated. But when an artiste renders these sounds or beats the intervals will not be uniform and will change randomly. Such versions can be captured making use of Simulation types.

If the total stage of upwards and downwards motion of the feet one particular time requires 30 seconds (say) at normal speed. It would take 20 seconds and 10 seconds in the 2nd and the third tempos. For case in point if tai happens at 0th instant, ya happens at the 13.5 seconds, tai is the hold out time for 3 seconds and hello happens at the 30th next, the upward motion of the ft lasts for 13.5 seconds and the downward movement lasts for 13.5 seconds and the wait around time lasts 3 seconds. A danseuse and a vocalist are unable to render such uniform motion to exactness as shown by the mathematical design and there could be variants.

The dancer’s or the artiste’s motion can be modelled by the situation of the torso in area or x,y,z co-ordinates and the relative motion of the Toes, Legs, Higher Hand, Lessen Hand, Arms head, neck and eyes with regard to the torso.

For a sequence of Tattu Adavu actions beginning at time t = and ending at time t = T the equation of the feet at an instantaneous time t is offered by the position of the torso of the dancer and the relative situation of the feet with respect to the Torso.

Because Tattu Adavu entails tapping of the toes and movement upwards the resultant motion of say the toes can be modelled employing algebra working with the subsequent discrete time equations ensuing in move features describing the motion. Differential equations can not be made use of as they would stand for a procedure that is continuous.

So crafting these equations of the Tattu Adavu as y = at t= y = h at t = T/2 and y = at at t = T the place T is the time period of a defeat and h is the maximum top arrived at by a foot. This can fixed at 30 cms or can be assorted in between 25 cms and 50 cms. This is the algebraic product of the 1st Tattu Adavu. In case a model of variation is to be used, then the algebraic model utilised must be changed with a simulation design.

The 2nd tattu adavu or the tapping of the feet with two situations per defeat can be modelled as y = at t= y = h at t = T/4 y = at t=T/2 y=h at t = 3T/4 y= at t = T.

If the locus of the ft is plotted for additional variety of details along the time interval then the identical equation can be described as y = at t= y = h/10 and t= T/10 y = h/9 at t = T/9 and so forth.

A dancer with normal movement will not be ready to replicate the correct mathematical congruence of the peak attained by the relocating feet with the regard to the divisions within just the time period of time of the Sollukattu.

If a person plots the actual movement of a dancers toes though performing the ‘tattu adavu'(translated in english as tapping of the feet) the resulting equation would be h = at t= , y = .6h at t= T/2 and h = 1.1h at t = T and so forth.

These algebraic equations can be applied to create pc applications which use graphics to design the movement of a classical dancer’s ft. Hence some factors of the mechanical actions or adavus can be routinely created centered on making use of correct designs to capture the motion of the toes.

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