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Wednesday, February 8, 2023

# Mathematical Modelling of Actions in BharathaNatyam

Mathematical modeling entails making products of true-entire world techniques working with mathematical tactics this kind of as linear programming, differential equations, and many others. When the technique product has inherent uncertainties, in addition to the mathematical product, simulation is utilised to depict a stationary or dynamic method (a system in movement).

Adavus in BharathaNatyam (an art variety of classical dance in southern India) represents a established of actions (nrityam) that do not include expression. For that reason, Adavus can be examined utilizing mathematical types.

Tattu Adavu entails raising the feet up and down so that one particular can hear the tapping.

“Sollukattu” (Tamil phrase translated into English, spoken as a defeat) is presented in unique rhythms. The feet also repeat movements in a variety of counts, this kind of as 4, 6, and 8.

The four verbal beats can be pronounced tai, ya, tai, hello. If four oral beats manifest at T(1), T(2), T(3), and T(4), the place T(I) is the ith moment that accompanies the artist to utter a verbal beat.

The tempo or cadence is specified by T(2) – T(1) T(3) – T(2) and T(4) – T(3). Preferably, all of these time intervals should really be equivalent. If these beats are machine-generated, they can be equivalent. But when the artist renders these seems or beats, the intervals will be uneven and will vary randomly. This kind of variations can be captured employing a simulation design.

If the entire action of shifting the foot up and down at a time at usual velocity requires 30 seconds (let’s say). The second and 3rd rhythms get 20 seconds and 10 seconds. For instance, if tai seems at time , ya appears at 13.5 seconds, tai is a waiting time of 3 seconds, and hello appears at 30 seconds, the upward motion of the foot lasts 13.5 seconds, and the downward movement lasts 13.5 seconds. The waiting around time lasts 3 seconds. . Dancers and singers are not able to stand for this uniform motion accurately as a mathematical model demonstrates, and there may perhaps be variation.

The movements of a dancer or entertainer can be modeled to the torso by the situation of the torso in space or by the x, y, z coordinates and the relative motion of the feet, legs, upper hands, decrease palms, arms, head, neck, and eyes.

For a series of Tattu Adavu techniques beginning at time t = and ending at time t = T, the equation for the ft at prompt time t is presented by the posture of the dancer’s torso and the relative posture of the ft to the torso.

Due to the fact Tattu Adavu entails tapping the foot and upward motion, the ensuing movement of the toe can be modeled algebraically utilizing the adhering to discrete-time equation, resulting in a action operate describing the movement. Differential equations are unable to be utilized since they will symbolize a continual system.

So, create these equations for Tattu Adavu as y = at t = y = h at t = T/2 and y = at at t = T where by T is the time period of time of the beat and h is the greatest height reached a foot. This can be mounted at 30cm or can fluctuate involving 25cm and 50cm. This is the 1st Tattu Adavu algebraic design. If a variation design is to be used, the algebraic design employed must be replaced by a simulation design.

A second tattu adavu or double foot faucet for every defeat can be modeled as y = at t= y = h at t = T/4 y = at t=T/2 y=h at At t = 3T/4 at t = T, y = .

If the trajectory of the foot is plotted for a lot more details together the time interval, the same equation can be described as y= at t= y=h/10 and t=T/10 y=h/9 at t= T/9 etc.

Dancers with all-natural actions will not be able to replicate the exact mathematical regularity of heights and divisions realized by shifting their toes in the Sollukattu time period.

If you plot the genuine movement of the dancer’s foot when doing “tattu adavu” (which translates to tapping of the foot in English), the ensuing equations will be h = at t= , y = .6h at t= T/2 and h = 1.1h at t = T and so on.

These algebraic equations can be utilised to produce computer system applications that use graphics to simulate the foot movements of classical dancers. Consequently, foot motion can be captured primarily based on working with an proper product to automatically create mechanical techniques or some component of the adavus.

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