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用物理解释芭蕾中最难的动作 – Arleen Sugano – 译学馆
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用物理解释芭蕾中最难的动作 - Arleen Sugano

The physics of the "hardest move" in ballet - Arleen Sugano

芭蕾舞“天鹅湖”第三幕中
In the third act of “Swan Lake,”
扮演黑天鹅的舞者成功完成了那一系列看似不停歇的旋转
the Black Swan pulls off a seemingly endless series of turns,
她用脚尖上下跳跃
bobbing up and down on one pointed foot
旋转 旋转 旋转32圈
and spinning around, and around, and around 32 times.
这是芭蕾舞中最难的动作之一
It’s one of the toughest sequences in ballet,
这个动作持续的时间超过30秒
and for those thirty seconds or so,
她就像个能够不停旋转的人
she’s like a human top in perpetual motion.
这些连续的旋转被称为fouettés
Those spectacular turns are called fouettés,
在法语中是“单足立地旋转”的意思
which means “whipped” in French,
用来描述舞者连续不停地旋转的神奇能力
describing the dancer’s incredible ability to whip around without stopping.
但在惊叹的同时 我们能够解释这种动作的物理原理吗?
But while we’re marveling at the fouetté, can we unravel its physics?
芭蕾舞者踮起脚尖 让脚形成一个转矩来开始旋转动作
The dancer starts the fouetté by pushing off with her foot to generate torque.
但困难的是 要不停地旋转
But the hard part is maintaining the rotation.
旋转时 踮起的脚尖与地面的摩擦力
As she turns, friction between her pointe shoe and the floor,
以及身体与空气产生的一些摩擦力
and somewhat between her body and the air,
会消耗她的体力
reduces her momentum.
那么 她是如何做到不停旋转的?
So how does she keep turning?
每次旋转时 舞者都会停顿一刹并面向观众
Between each turn, the dancer pauses for a split second and faces the audience.
她将踮起的脚放平
Her supporting foot flattens,
然后在重新踮起脚尖时 用力一转
and then twists as it rises back onto pointe,
对地面施以推力 来形成一个新的微型转矩
pushing against the floor to generate a tiny amount of new torque.
同时 她也张开双手舞动来保持平衡
At the same time, her arms sweep open to help her keep her balance.
如果重心稳的话 旋转起来的效果是最好的
The turns are most effective if her center of gravity stays constant,
技艺高超芭蕾舞者能垂直轴心旋转
and a skilled dancer will be able to keep her turning axis vertical.
张开的双手和形成转矩的脚
The extended arms and torque-generating foot
都能帮助她旋转
both help drive the fouetté.
但你很难发现其停顿的真正秘诀和原因
But the real secret and the reason you hardly notice the pause
在于 她的另一条腿从没停过
is that her other leg never stops moving.
在短暂的停顿中
During her momentary pause,
收回腿之前 她将那条腿伸直抬高
the dancer’s elevated leg straightens and moves from the front to the side,
从前面往一侧伸展
before it folds back into her knee.
她的那条腿稍微停顿后 又能恢复旋转的体力
By staying in motion, that leg is storing some of the momentum of the turn.
收回伸出的另一条腿时
When the leg comes back in towards the body,
芭蕾舞者又恢复了体力
that stored momentum gets transferred back to the dancer’s body,
又能重新踮起脚尖旋转了
propelling her around as she rises back onto pointe.
芭蕾舞者每次旋转时都要伸出和收回另一条腿
As the ballerina extends and retracts her leg with each turn,
这样才能恢复腿部和身体的力量
momentum travels back and forth between leg and body,
来继续旋转
keeping her in motion.
真正优秀的芭蕾舞者 用一到两种方法 就能
A really good ballerina can get more than one turn out of every leg extension
在每次伸出另一条腿后 多转几圈
in one of two ways.
第一种方法就是 她可以快速伸出一条腿
First, she can extend her leg sooner.
那条腿伸出的时间越长 另一条腿恢复的力量就越多
The longer the leg is extended, the more momentum it stores,
收回那条腿时 恢复的体力也越多
and the more momentum it can return to the body when it’s pulled back in.
在需要补充由摩擦消耗的动力之前
More angular momentum means she can make more turns
角动量越大 意味着她能转的圈数越多
before needing to replenish what was lost to friction.
第二种方法是
The other option is for the dancer
芭蕾舞者要转圈时 会将双手
to bring her arms or leg in closer to her body
和腿收拢一点
once she returns to pointe.
为什么这种方法会有用?
Why does this work?
跟芭蕾舞中其他的旋转动作一样
Like every other turn in ballet,
旋转是由角动量决定的
the fouetté is governed by angular momentum,
角动量等于舞者的角速度乘以她的旋转惯量
which is equal to the dancer’s angular velocity times her rotational inertia.
如果不考虑摩擦中消耗的动力
And except for what’s lost to friction,
在芭蕾舞者踮起脚尖时 角动量要保持不变
that angular momentum has to stay constant while the dancer is on pointe.
这称为角动量守恒
That’s called conservation of angular momentum.
现在 旋转惯量可以看作是
Now, rotational inertia can be thought of
身体旋转的阻力
as a body’s resistance to rotational motion.
旋转的物体离旋转轴越远 旋转惯量就会变大
It increases when more mass is distributed further from the axis of rotation,
旋转物体离旋转轴越近 旋转惯量就会越小
and decreases when the mass is distributed closer to the axis of rotation.
所以芭蕾舞者将她的双臂和腿收拢
So as she brings her arms closer to her body,
那么她受到的阻力就会变小
her rotational inertia shrinks.
为了遵循角动量守恒定律
In order to conserve angular momentum,
她的角速度 即旋转的速度
her angular velocity, the speed of her turn,
要加快
has to increase,
这样才能保持角动量的数值
allowing the same amount of stored momentum
增加旋转的圈数
to carry her through multiple turns.
你可能见过溜冰的人也做这样的动作
You’ve probably seen ice skaters do the same thing,
他们旋转地越来越快的同时 也在收拢双手和双腿
spinning faster and faster by drawing in their arms and legs.
在柴可夫斯基的芭蕾舞剧《天鹅湖》中 黑天鹅是一个女巫
In Tchaikovsky’s ballet, the Black Swan is a sorceress,
她的32圈优美的单足立地旋转 看起来就像是超自然力量
and her 32 captivating fouettés do seem almost supernatural.
但这不是通过魔法来实现的
But it’s not magic that makes them possible.
这是通过物理原理来实现的
It’s physics.

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视频概述

芭蕾舞中神奇的32圈单足立地旋转虽然让人觉得不可思议,但还是可以用物理原理解释

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