How to get the constraint equation of this problem

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In summary, a particle is constrained to move in the xy plane with its velocity always directed towards a point on the x-axis, determined by a given function of time f(t). This constraint is considered nonholonomic for f(t) differentiable, regardless of its other properties.
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A particle moves in the xy plane under the constraint that its velocity vector is always directed towards a point on the x-axis whose abscissa is some given function of time f(t). Show that for f(t) differentiable, but otherwise arbitrary, the constraint is nonholonomic.
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it have cost me 3 hours,but i cann't write out the constraint equation :confused: .
help
thanks
 
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goodboy said:
A particle moves in the xy plane under the constraint that its velocity vector is always directed towards a point on the x-axis whose abscissa is some given function of time f(t). Show that for f(t) differentiable, but otherwise arbitrary, the constraint is nonholonomic.
--------------------------------------------
it have cost me 3 hours,but i cann't write out the constraint equation :confused: .
help
thanks

https://www.physicsforums.com/showthread.php?t=138432&highlight=holonomic
 

1. What is a constraint equation in a scientific problem?

A constraint equation in a scientific problem is an equation that represents a limitation or condition that must be satisfied in order to solve the problem. It is usually derived from physical laws or principles that govern the system being studied.

2. How do you determine the constraint equation in a problem?

The constraint equation can be determined by identifying the relevant physical laws or principles that apply to the problem. These can include conservation laws, equilibrium conditions, or other mathematical relationships that govern the behavior of the system.

3. Can a constraint equation be derived mathematically?

Yes, a constraint equation can be derived mathematically by using mathematical tools such as calculus, linear algebra, or other mathematical techniques. These tools can help to express the physical laws or principles in mathematical form, which can then be used to derive the constraint equation.

4. What is the purpose of a constraint equation in a scientific problem?

The purpose of a constraint equation is to provide a mathematical representation of the limitations or conditions that must be satisfied in order to solve the problem. It helps to define the boundaries of the problem and guide the solution process.

5. Are there different types of constraint equations in scientific problems?

Yes, there are different types of constraint equations depending on the type of problem being studied. For example, in mechanics, constraint equations may involve forces, velocities, and accelerations, while in thermodynamics, they may involve energy, temperature, and entropy. The specific type of constraint equation used will depend on the nature of the problem.

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