Why are the equations of motion second order?

Many equations of motion are second order in d/dt because the net force acting on an object determines in ts acceleration. So if you know the (net) force, you know the value of . A general equation which represents motion of a body will be a second order equation in time derivative.

Why is TDSE first order in time?

In partial differential equations, there can be multiple independent variables, so you have to specify which one you’re talking about — hence the “in time” part. Thus, first-order in time means just one derivative with respect to time. The classic example is the basic one-dimensional heat equation: ∂ϕ∂t=∂2ϕ∂x2 .

Are Lagrangians with only higher order derivative terms fatal?

It is shown that Lag- rangians containing only higher order derivative terms are fatal, possibly with the exception of the case there a third derivative enters linear. For this case and for the case where a second order Lagrangian is added to a linear third order Lagrangian, conditions are found, but not yet solved. Contents

Is there a way to write higher order Lagrangians?

For classical mechanics there are (under certain conditions) possibilities to write higher order Lagrangians, but the higher order terms can be taken into total derivatives, meaning all these possibilities are in fact equivalent to \\frst order Lagrangians and are therefore, in the context of this research, trivial.

What is the difference between Lagrangian mechanics and Newtonian mechanics?

The reason Newtonian mechanics is still the pre- ferred choice in secondary school is simple the fact the Lagrangian formulation is more abstract an the fact that students are not yet comfortable with (partial) di\erentiation. However, for the theoretical physicist it is much more useful and often the preferred choice.

Which Lagrangians produce workable equations of motion?

Normally only \\frst order Lagrangians produce workable equations of motion, because higher order Lagrangians con- tain ghost degrees of freedom (i.e. the Hamiltonian contains a term linearly in momentum, meaning it is unbounded.), as shown by Ostrogradski.