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Mathematical Modelling entails making a mannequin of an actual world system utilizing strategies in Arithmetic comparable to Linear Programming, Differential Equations and so forth. When the system mannequin has inherent uncertainty, simulation is used along with the Mathematical Mannequin to characterize both a stationary or a dynamic system (System in Movement).
Adavus in BharathaNatyam (Classical dance artwork type of south India) characterize a set of steps which don’t contain expression (nrityam). So Adavus could be studied utilizing Mathematical Fashions.
Tattu Adavu entails lifting the toes up and down in order that one can hear the tapping noise.
The “sollukattu”(tamil phrase translated into English as Verbal pronunciation of beats) is rendered in various tempos. There are additionally repeated motion of the toes in numerous counts comparable to 4,6 and eight.
The 4 verbal beats could be pronounced as tai,ya, tai,hello. If the 4 verbal beats happen at T(1), T(2), T(3) and T(4) the place T(I) is the ith instantaneous 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 needs to be equal. It may be equal if these beats are machine generated. However when an artiste renders these sounds or beats the intervals is not going to be uniform and can differ randomly. Such variations could be captured utilizing Simulation fashions.
If the whole step of upwards and downwards motion of the toes one time takes 30 seconds (say) at regular pace. It could take 20 seconds and 10 seconds within the second and the third tempos. For instance if tai happens at 0th instantaneous, ya happens on the 13.5 seconds, tai is the wait time for 3 seconds and hello happens on the thirtieth second, the upward movement of the toes lasts for 13.5 seconds and the downward movement lasts for 13.5 seconds and the wait time lasts 3 seconds. A danseuse and a vocalist can not render such uniform movement to exactness as demonstrated by the mathematical mannequin and there could also be variations.
The dancer’s or the artiste’s motion could be modelled by the place of the torso in house or x,y,z co-ordinates and the relative movement of the Toes, Legs, Higher Hand, Decrease Hand, Arms head, neck and eyes with respect to the torso.
For a sequence of Tattu Adavu steps beginning at time t = 0 and ending at time t = T the equation of the toes at an instantaneous time t is given by the place of the torso of the dancer and the relative place of the toes with respect to the Torso.
Since Tattu Adavu entails tapping of the toes and motion upwards the resultant movement of say the toes could be modelled utilizing algebra utilizing the next discrete time equations leading to step features describing the movement. Differential equations can’t be used as they’d characterize a system that’s steady.
So writing these equations of the Tattu Adavu as y =0 at t= 0 y = h at t = T/2 and y = 0 at at t = T the place T is the time interval of a beat and h is the utmost peak reached by a foot. This could fastened at 30 cms or could be different between 25 cms and 50 cms. That is the algebraic mannequin of the first Tattu Adavu. In case a mannequin of variation is for use, then the algebraic mannequin used needs to be changed with a simulation mannequin.
The second tattu adavu or the tapping of the toes with two instances per beat could be modelled as y =0 at t=0 y = h at t = T/4; y = 0 at t=T/2; y=h at t = 3T/4; y= 0 at t = T.
If the locus of the toes is plotted for extra variety of factors alongside the time interval then the identical equation could be described as y = 0 at t= 0; y = h/10 and t= T/10; y = h/9 at t = T/9 and so forth.
A dancer with pure movement will be unable to duplicate the precise mathematical congruence of the peak attained by the shifting toes with the respect to the divisions inside the time interval of the Sollukattu.
If one plots the precise movement of a dancers toes whereas performing the ‘tattu adavu'(translated in english as tapping of the toes) the ensuing equation could be h = 0 at t= 0, y = 0.6h at t= T/2 and h = 1.1h at t = T and so forth.
These algebraic equations can be utilized to jot down pc packages which use graphics to mannequin the movement of a classical dancer’s toes. Therefore some elements of the mechanical steps or adavus could be mechanically generated primarily based on utilizing applicable fashions to seize the motion of the toes.
