Covariant & Contravariant Components

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SUMMARY

The discussion focuses on transforming a vector A = i xy + j (2y-z²) + k xz from rectangular coordinates to spherical coordinates, specifically into covariant and contravariant components. Participants clarify the definitions of coordinate basis vectors and unit vectors in spherical coordinates, emphasizing the relationships between them. The conversation highlights the importance of understanding these transformations and the algebra involved in deriving the correct components.

PREREQUISITES
  • Understanding of vector transformations in spherical coordinates
  • Familiarity with covariant and contravariant components
  • Knowledge of coordinate basis vectors and unit vectors
  • Basic algebra and calculus skills for manipulating vector equations
NEXT STEPS
  • Study the transformation equations for vectors in spherical coordinates
  • Learn about the relationship between covariant and contravariant components
  • Explore examples of vector transformations in orthogonal coordinate systems
  • Review the concept of reciprocal basis vectors and their applications
USEFUL FOR

Students in physics or engineering, particularly those studying vector calculus, anyone needing to understand vector transformations in spherical coordinates, and educators seeking to clarify these concepts for their students.

  • #31
Ok do you mind if I try and solve those and then show them too you to see if I completely understand now?
 
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  • #32
Biffinator87 said:
Ok do you mind if I try and solve those and then show them too you to see if I completely understand now?
No problem. But the hard part was over once you found the components in terms of the unit vectors. That was before we even started talking about covariant and contravariant.

Chet
 

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