Equation of motion from matrix

In summary, the equation of motion from a matrix is a mathematical representation of an object's position, velocity, and acceleration. It is derived using principles of linear algebra and matrix multiplication, and offers advantages such as compactness and flexibility. It can also be used for non-linear systems and has many real-world applications in fields such as robotics and aerospace engineering.
  • #1
intervoxel
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1
How can I find the equation of motion of a system with the Hamiltonian in matrix form?
 
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  • #2
I assume given the nature of the question you are adept with the mathematics but I am unsure if you are dealing with a quantum or classical mechanics problem. If it is classical you need to use a Poisson bracket see http://ocw.mit.edu/ans7870/18/18.013a/textbook/chapter16/section03.html
If it is a quantum problem then decompose the matrix in Dirac bra and ket eigenvectors
 
  • #3
Thank you.
 

FAQ: Equation of motion from matrix

What is the equation of motion from a matrix?

The equation of motion from a matrix is a mathematical representation of the relationship between an object's position, velocity, and acceleration. It is often used in physics and engineering to describe the motion of a system.

How is the equation of motion derived from a matrix?

The equation of motion is derived from a matrix by applying the principles of linear algebra and using matrix multiplication to represent the different components of motion. It is a concise and elegant way of representing complex motion equations.

What are the advantages of using a matrix to represent the equation of motion?

Using a matrix to represent the equation of motion has several advantages. It allows for a compact representation of complex motion equations, making it easier to manipulate and solve. It also allows for the incorporation of multiple variables and parameters, making it a more flexible and versatile tool.

Can the equation of motion from a matrix be used for non-linear systems?

Yes, the equation of motion from a matrix can be used for non-linear systems as well. However, in these cases, the matrix may need to be updated over time to account for changes in the non-linear behavior of the system.

How is the equation of motion from a matrix used in real-world applications?

The equation of motion from a matrix is used in a wide range of real-world applications, including robotics, aerospace engineering, and computer graphics. It is a powerful tool for simulating and predicting the motion of objects and systems, making it essential in many industries and fields of study.

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