来自《耶鲁大学开放课程：基础物理 第7集 第7集》

• 
  
  U1 is shorthand for U of x1;
  U1 是 U(x1) 的简写
• 
  
  is K2 + U2.
  等于 K2 + U2
• 
  
  And that means the energy E1 to begin with, the energy at the end.
  这表示初态能量 E1 和末态能量
• 
  
  If there is a frictional force,
  如果存在摩擦力
• 
  
  then in this integral you break it up into two parts:
  那么这个积分可以分成两部分
• 
  
  the part, say, due to a spring and the part due to friction.
  一部分关于弹簧 另一部分关于摩擦力
• 
  
  The part due to a spring will integrate to give you this.
  弹簧部分的积分得到这个结果
• 
  
  Then, you'll still have the part due to friction left over.
  然后 还要加上摩擦部分
• 
  
  In that case the result will look like
  这种情况下
• 
  
  Instead of being zero,
  不再等于零
• 
  
  it will be the work done by friction.
  而等于摩擦力所做的功
• 
  
  We write it symbolically this way
  我们象征性地将它写成这样