Non holonomic constraints in classical mechanics refer to restrictions on the motion of a system that cannot be described by a set of independent generalized coordinates. These constraints are typically expressed as inequalities or differential equations, and they limit the possible motions of a system.
Non holonomic constraints affect the equations of motion by introducing additional terms that account for the constraints. These terms are often referred to as constraint forces or Lagrange multipliers, and they are necessary to ensure that the system satisfies the constraints while still following the laws of motion.
The main difference between holonomic and non holonomic constraints is that holonomic constraints can be expressed as a set of independent equations, while non holonomic constraints cannot. Holonomic constraints also do not introduce any additional terms in the equations of motion, while non holonomic constraints do.
In general, non holonomic constraints cannot be removed. However, in some cases, they can be approximated or replaced with holonomic constraints that have a similar effect. This is known as constraint approximation or constraint relaxation, and it is often used in practical applications of classical mechanics.
Non holonomic constraints are used in a variety of real-world applications, such as robotics, vehicle dynamics, and control systems. They are particularly useful for describing systems with rolling or sliding constraints, such as wheeled vehicles or moving platforms. Non holonomic constraints can also be used to model complex mechanical systems, such as those found in biomechanics or fluid dynamics.