The D'Alembert's Principle states that:
[itex] \sum_s [\underline{ F_s^{applied}} - \frac{d}{dt} (\underline{p_s}) ] \cdot \underline{δr_s} = 0 [/itex]
s - labels particles
That is when [itex] F_s [/itex] doesn't include the constraint forces, and the virtual displacement is reversible, and compatible with the constraints.
My question is - doesn't it just say that:
- if there are no constraints, Newton's laws are obeyed, with force being [itex] F_s [/itex] - (the parenthesis is zero)
- if there are holonomic constraints, we can only displace the object perpendicular to the constraint forces - (the dot product is zero)
?
Does this principle also say something about non-holonomic constraints? And if so, can anyone give an example?
And what exactly is the difference between reversible and irreversible virtual displacement? If a displacement is virtual, and if displacing by dx is possible, then also displacing back by -dx should be possible. So how can we have an irreversible displacement at all?
[itex] \sum_s [\underline{ F_s^{applied}} - \frac{d}{dt} (\underline{p_s}) ] \cdot \underline{δr_s} = 0 [/itex]
s - labels particles
That is when [itex] F_s [/itex] doesn't include the constraint forces, and the virtual displacement is reversible, and compatible with the constraints.
My question is - doesn't it just say that:
- if there are no constraints, Newton's laws are obeyed, with force being [itex] F_s [/itex] - (the parenthesis is zero)
- if there are holonomic constraints, we can only displace the object perpendicular to the constraint forces - (the dot product is zero)
?
Does this principle also say something about non-holonomic constraints? And if so, can anyone give an example?
And what exactly is the difference between reversible and irreversible virtual displacement? If a displacement is virtual, and if displacing by dx is possible, then also displacing back by -dx should be possible. So how can we have an irreversible displacement at all?