User Tools

Site Tools


formalisms

Differences

This shows you the differences between two versions of the page.

Link to this comparison view

Both sides previous revision Previous revision
formalisms [2018/05/06 07:23]
jakobadmin
formalisms [2019/08/12 18:37] (current)
95.91.233.167 [Formalisms]
Line 19: Line 19:
  
 ^ Lagrangian formalism ​                                                                                                                                             ^ Hamiltonian formalism ​                                                                                                                              ^ ^ Lagrangian formalism ​                                                                                                                                             ^ Hamiltonian formalism ​                                                                                                                              ^
-| We describe the state of a system with $n$ degrees of freedom with the $n$ coordinates $(q_1,​\ldots,​ q_n)$ and the $n$ velocities $(\dot{q}_1,​\ldots , \dot{q}_n)$ ​ | We describe the state the a system with $n$ degrees of freedom by the $n$ coordinates $(q_1,​\ldots,​ q_n)$ and the $n$ momenta $(p_1,​\ldots , p_n)$  |+| We describe the state of a system with $n$ degrees of freedom with the $n$ coordinates $(q_1,​\ldots,​ q_n)$ and the $n$ velocities $(\dot{q}_1,​\ldots , \dot{q}_n)$ ​ | We describe the state of a system with $n$ degrees of freedom by the $n$ coordinates $(q_1,​\ldots,​ q_n)$ and the $n$ momenta $(p_1,​\ldots , p_n)$  |
 | We represent the //state// of the system by a point moving with a definite velocity in an $n$-dimensional configuration space | We represent the //state// of the system by a point moving with a definite velocity in an $2n$-dimensional phase space with coordinates $(q_1,​\ldots,​ q_n; p_1,\ldots , p_n)$ | | We represent the //state// of the system by a point moving with a definite velocity in an $n$-dimensional configuration space | We represent the //state// of the system by a point moving with a definite velocity in an $2n$-dimensional phase space with coordinates $(q_1,​\ldots,​ q_n; p_1,\ldots , p_n)$ |
 | The $n$ configuration space coordinates evolve according to $n$ second-order equations | The $2n$ phase space coordinates evolve according to $2n$ first-order equations | | The $n$ configuration space coordinates evolve according to $n$ second-order equations | The $2n$ phase space coordinates evolve according to $2n$ first-order equations |
formalisms.txt · Last modified: 2019/08/12 18:37 by 95.91.233.167