The Physics of Bharatanatyam
by Kavvinah Murali
yato hasta tato dhṛiṣhṭi (Where the hands go, the eyes follow)
yato dhṛiṣhṭi tato manaḥ (Where the eyes go, the mind follows)
yato manaḥ tato bhāva (Where the mind goes, expressions are made)
yato bhāva tato rasaḥ (Where there are expressions, emotion is evoked)
Bharatanātyam (pronounced: Bha-ra-tha-naatt-yam) is one of the oldest traditional dance forms encompassing rhythmic movement, rigid postures, and strenuous footwork accompanied by Carnatic Music. The use of hand gestures, facial expressions, and body language aid in expressing a myriad of nuanced emotions in Bharatanatyam storytelling.
When I was younger, I developed a habit of closely observing other classical dancers, especially Kalakshetra Bharatanatyam dancers, to improve my dance technique. Squatting a little lower, bending a little further, and leaping a little higher were minute corrections that I focused on in order to achieve my childhood dream of becoming a talented dancer like them one day.
Growing up, I quickly realised that my dream of becoming a renowned dancer seemed a little far-fetched as the societal expectation for me to excel academically and take up a “professional job” grew stronger. However, even in the comforts of the Physics lab, in the back of my mind, I would still be going through a recent choreography I learnt: my hands forming mudras (hand gestures) under the table and my feet tapping the floor to the beats of the Mridangam (Indian percussion instrument) playing in my head.
On one particular day in Physics class, as we were learning about Forces and Motion, I started questioning why squatting a little lower, bending a little further, and leaping a little higher made Bharatanatyam more aesthetically pleasing. How did Bharatanatyam dancers make fast-paced, complex, and intricate dance moves seem so easy to perform? How much does dance have to do with Physics, Mechanics and Human Anatomy?
Before exploring the connection between these fields of knowledge, let us first understand the origin of Bharatanatyam.
The Origin of Bharatanatyam
Bha stands for Bhāvam (Emotion),
Ra stands for Rāgam (Melody/Music),
Ta stands for Tālam (Rhythm),
Nātyam means Dance.
Indian Classical dance forms date to 500 BC when Sage Bharata Muni first wrote the Nāṭyaśāstra (pronounced: Naat-ya-shaas-tra): The Ancient Scripture of Indian Classical Dances (Natyashastra | Indian Drama Treatise, n.d. & What Is the Natyashastra?, 2022). As a comprehensive dance and theatre manual, the Nāṭyaśāstra dedicates a chapter that details 108 Karanas (coordinated movements of arms and legs) which form the basis of adavus (basic dance steps) in Bharatanatyam and many other Indian classical dance forms (What Are Karanas?, 2022).
Another treatise called the Abhinaya Darpana by Nandikeshwarar is known to be a simplified version of the Nāṭyaśāstra, meticulously curated for Bharatanatyam (Nandikeshwara’s Abhinaya Darpana, n.d.). The Abhinaya Darpana describes Bhedas (movement patterns for different body parts) in a continuous series of poems. These Bhedas include Shirobheda (head movements), Dhrishtibheda (eye movements), Greevabheda (neck movements), and Paadabheda (leg movements) (paadabheda — Natyarambha, 2014).
In this article, we will be deciphering the Physics of some Bhedas from the Abhinaya Darpana that form the aesthetics of Bharatanatyam.
The Physics of Bharatanatyam
Centre of Mass in Araimandi (Half-Squat)
The most basic Bharatanatyam stance that many Indian Classical dancers dread is the Araimandi (half-squat). To form the Araimandi, a dancer must align their arms, knees, torso, and feet to create a series of triangles in space that ensures the dancer dances with the right posture (Anatomy of the Araimandi — Hektoen International, 2022). As painful as it is to squat with knees to the side, the Araimandi helps improve a dancer’s stability while dancing. This can be explained by understanding the Centre of Mass (COM) of objects.
The COM of an object is an imaginary point at which the entire mass of the object is assumed to act upon. In some cases, the COM of an object may even be outside the body of an object.
An object is said to be stable when it does not easily topple. For toppling to occur, the object needs to be tilted past its COM (Center of Mass and Stability, 2012). In other words, the lower the COM of an object, the more difficult it is to topple, hence, the more stable the object is.
A human’s COM is around the navel area at a ratio that ranges from 0.543~0.560 of the person’s height (Elert, n.d.), which is approximately the geometric centre of the human body. Dancers maintain balance by positioning their body’s COM over their base of support: their feet (“Physics in Dance and Dance to Represent Physical Processes,” 2011).
As depicted in Figure 1, the application of Physics tells us that sitting in Araimandi lowers the dancer’s centre of mass. Hence, this makes the dancer more stable.
With enough muscle training and practice, the Araimandi stance can be mastered and the core strength that comes along with it keeps the dancer’s body in a healthy posture and prevents dangerous falls while dancing.
Torque in the Bhramari Bheda (Turns)
Like Pirouettes in Ballet, it is noticeable that many dance forms include variations of leg extensions when the dancer makes impressive spins and turns. As an initial force is applied and the dancer stretches their leg out perpendicular to their body, a moment of force, also known as torque, is produced.
Torque is a force’s tendency to cause a turning effect or rotation about a specific point (fulcrum or pivot). Torque is defined as the product of the force applied (perpendicular to the fixed point) and the distance of the applied force from the fixed point.
In simpler words, Torque = Force x distance
Figure skaters are great examples to illustrate the application of rotational angular momentum (Youtube: Angular Momentum V2: Physics Concept TrailerTM, 2015).
Due to the Principle of Conservation of Momentum, for as long as the distance of force on the leg is constant, the skater would ideally spin at the same angular velocity (speed) if there is no external resistance (Conservation of Angular Momentum, 2015). When the figure skater fully stretches their leg out, they spin slowly, and they begin to spin faster when their legs are folded in.
Similarly, when performing Kunchita Bharmari in Bharatanatyam, the dancer gradually bends their knee and pulls the leg back towards the body to reduce torque. When distance reduces, torque and angular momentum reduces too, and the dancer stops spinning.
Newton’s Laws of Motion in the Utplavana Bheda (Leaps and jumps)
When a dancer softly breaks contact with the floor, projecting their body toward the sky, that mid-air moment, even if only a few milliseconds long, will surely keep the audience at the edge of their seats.
To add dimension to the performance, Bharatanatyam dancers perform jumps and leaps when sufficient force produced by their muscles lifts them from the floor. Newton’s laws of motion are essential to understanding and explaining the forces involved.
Newton’s Second Law of Motion
Newton’s second law of motion states that the rate of change of momentum is directly proportional to the force exerted on an object.
Force = Mass x Acceleration.
In simpler words, when unbalanced forces act on an object, the object starts moving (accelerating) in a certain direction. This is important to initiate the jump.
Newton’s Third Law of Motion
Newton’s third law states that when a force is acted upon an object, a force of equal magnitude will be produced but acting in the opposite direction from it to balance the forces out.
In simpler terms, every action has an equal and opposite reaction. When the dancer exerts a force on the floor, the floor provides an equal thrust force on the dancer for the jump to happen (“Physics in Dance and Dance to Represent Physical Processes,” 2011).
Understanding the Forces Involved in Jumps and Leaps
The force generated in the leg muscles (quadriceps, hamstrings, and calves) to initiate the jump must be more than the weight of the dancer to produce a lift. Only when the upward force is more than the downward force will the dancer be able to lose contact with the ground.
At the highest point of the jump, the dancer remains stationary for a millisecond because the upward and downward forces are balanced, and upward acceleration equals zero. However, immediately after that, the downward force becomes more than the upward force due to gravity, which makes the dancer return down instead of continuously being projected upwards.
As the dancer lands, they bend their knees (in the Araimandi position) and land on their toes first to increase landing time (also known as the time of impact). The time of impact is inversely proportional to the impulsive force.
This means that when the time of impact increases, the impulsive force acting on the knees and ankles decreases. Thus, both knee and ankle injuries can be prevented.
Since the land is softer, it also adds to the grace of the dance.
Projectile Motion When Jumping
This sideway Bharatanatyam jump uses the same principles of movement of a Grand Jeté (split jump) in Ballet. Based on the experimental findings in Physics in Dance and Dance to Represent Physical Processes (2011), the analysis of the experimental video shooting enabled the authors to point out the almost horizontal motion of the head and body of the ballerina compared to the parabolic motion of their centre of mass.
The parabolic curve of movement experienced by the Bharatanatyam dancer during this Motita Utplavana jump is known as projectile motion. Projectile motion is achieved when a horizontal and vertical force is exerted on the dancer which combines as the net upward and forward force whilst being pulled down by gravitational force (gravity) for the dancer to return to the ground.
This parabolic pathway of the Bharatanatyam dancer during a jump or leap creates an illusion of a floating dancer and makes the dance seem light.
Conclusion
The question of how Bharata Muni and Nandikeshwarar, from over 2,500 years ago, composed intricate musical, mathematical, and scientific theatre literature is intriguing. Did our ancestors dance with the technical and physiological awareness behind every dance move, or did they dance merely for its aesthetics and theatrical aspect?
Ultimately, we might not know the answer to this question, but this article proves that there is a common denominator between Science and Art: the freedom to express ideas. Both scientists and artists strive to understand how the world around them works and discover new ways to communicate their ideas creatively for us all to appreciate the beautiful world we live in.
I ask as a dancing engineer, the next time you have to pick between science and art, why not both?
References
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