{"id":11169,"date":"2026-06-07T15:11:23","date_gmt":"2026-06-07T15:11:23","guid":{"rendered":"https:\/\/www.vedprep.com\/exams\/?p=11169"},"modified":"2026-06-07T15:12:19","modified_gmt":"2026-06-07T15:12:19","slug":"hamiltons-canonical-equations","status":"publish","type":"post","link":"https:\/\/www.vedprep.com\/exams\/csir-net\/hamiltons-canonical-equations\/","title":{"rendered":"Hamilton&#8217;s canonical equations For CSIR NET"},"content":{"rendered":"<h1>Hamilton\u2019s canonical equations For CSIR NET: A Comprehensive Guide<\/h1>\n<p><strong>Direct Answer: <\/strong>Hamilton\u2019s canonical equations For CSIR NET are a set of equations in classical mechanics that describe the time evolution of a physical system, derived from the principle of least action and widely applied in mechanics, optics, and other fields. Understanding these equations is <strong>critical <\/strong>for students preparing for competitive exams like CSIR NET, IIT JAM, and GATE, where Hamilton\u2019s canonical equations For CSIR NET play a vital role.<\/p>\n<h2>Introduction to Hamilton\u2019s canonical equations For CSIR NET<\/h2>\n<p>The topic of Hamilton\u2019s canonical equations falls under the unit <strong>Classical Mechanics <\/strong>of the CSIR-NET Mathematical Sciences syllabus. This unit is <strong>crucial <\/strong>for students preparing for CSIR NET, IIT JAM, and GATE exams, where Hamilton\u2019s canonical equations For CSIR NET are frequently asked. Hamilton\u2019s canonical equations For CSIR NET form the backbone of classical mechanics.<\/p>\n<p>Students can find detailed explanations of Hamilton\u2019s canonical equations in standard textbooks such as <em>Goldstein, Classical Mechanics <\/em>and <em>Landau and Lifshitz, Mechanics<\/em>. These textbooks provide <strong>detailed <\/strong>coverage of the subject, including the derivation and application of Hamilton\u2019s canonical equations For CSIR NET. This coverage is essential for a deep understanding of Hamilton\u2019s canonical equations For CSIR NET.<\/p>\n<p>Hamilton\u2019s canonical equations For CSIR NET are a set of fundamental equations in classical mechanics that describe the time evolution of a physical system. They are widely used in various fields, including physics, engineering, and mathematics, making Hamilton\u2019s canonical equations For CSIR NET a <strong>required <\/strong>topic. The equations have numerous applications; they are used to study the behavior of complex systems, and their understanding is crucial for solving problems in mechanics and optics.<\/p>\n<h2>Hamilton\u2019s canonical equations For CSIR NET<\/h2>\n<p>Hamilton\u2019s equations describe the time evolution of a physical system, making Hamilton\u2019s canonical equations For CSIR NET a fundamental concept in classical mechanics. These equations provide a powerful framework for understanding the dynamics of various physical systems, which is essential for mastering Hamilton\u2019s canonical equations For CSIR NET. Students should focus on key subtopics such as Lagrange\u2019s equations, the principle of least action, and the Legendre transformation.<\/p>\n<p>The equations are derived from the <strong>principle of least action<\/strong>, a variational principle that states the action of a physical system is minimized over a given time interval. This principle, also known as the <em>action principle<\/em>, is a cornerstone of classical mechanics and is closely related to Hamilton\u2019s canonical equations For CSIR NET. The derivation of Hamilton\u2019s canonical equations For CSIR NET involves several steps; it requires a deep understanding of the Lagrangian and Hamiltonian functions.<\/p>\n<p>Hamilton\u2019s canonical equations For CSIR NET have wide applications in <strong>mechanics<\/strong>, <strong>optics<\/strong>, and other fields. They are particularly useful for solving problems involving <code>conservative systems<\/code>, where the total energy remains constant over time. The equations are given by:<\/p>\n<ul>\n<li>$\\dot{q}_i = \\frac{\\partial H}{\\partial p_i}$<\/li>\n<li>$\\dot{p}_i = -\\frac{\\partial H}{\\partial q_i}$<\/li>\n<\/ul>\n<p>where $q_i$ and $p_i$ are the generalized coordinates and momenta, and $H$ is the <strong>Hamiltonian <\/strong>function, which represents the total energy of the system and is a key concept in Hamilton\u2019s canonical equations For CSIR NET.<\/p>\n<h2>Derivation of <a href=\"https:\/\/en.wikipedia.org\/wiki\/Hamiltonian_mechanics\" rel=\"nofollow noopener\" target=\"_blank\">Hamilton\u2019s canonical equations<\/a> For CSIR NET<\/h2>\n<p>A simple harmonic oscillator has a Lagrangian given by $L = \\frac{1}{2}m\\dot{q}^2 &#8211; \\frac{1}{2}m\\omega^2q^2$, where $m$ is the mass, $\\omega$ is the angular frequency, $q$ is the position, and $\\dot{q}$ is the velocity. The Hamiltonian $H$ is defined as the Legendre transform of $L$, which leads to $H = \\frac{p^2}{2m} + \\frac{1}{2}m\\omega^2q^2$, where $p$ is the momentum and is essential for understanding Hamilton\u2019s canonical equations For CSIR NET. This transformation is a crucial step in deriving Hamilton\u2019s canonical equations For CSIR NET.<\/p>\n<p>The Hamilton\u2019s canonical equations are given by $\\dot{q} = \\frac{\\partial H}{\\partial p}$ and $\\dot{p} = -\\frac{\\partial H}{\\partial q}$. For the simple harmonic oscillator, these equations become $\\dot{q} = \\frac{\\partial H}{\\partial p} = \\frac{p}{m}$ and $\\dot{p} = -\\frac{\\partial H}{\\partial q} = -m\\omega^2q$, demonstrating the application of Hamilton\u2019s canonical equations For CSIR NET. Solving these differential equations requires a good grasp of Hamilton\u2019s canonical equations For CSIR NET.<\/p>\n<p>Solving these differential equations, the time evolution of the oscillator&#8217;s position and momentum can be obtained. The solutions are $q(t) = q_0\\cos(\\omega t) + \\frac{p_0}{m\\omega}\\sin(\\omega t)$ and $p(t) = p_0\\cos(\\omega t) &#8211; m\\omega q_0\\sin(\\omega t)$, where $q_0$ and $p_0$ are the initial position and momentum, illustrating the use of Hamilton\u2019s canonical equations For CSIR NET. These solutions have numerous applications in physics and engineering.<\/p>\n<h2>Misconception: Hamilton\u2019s canonical equations For CSIR NET<\/h2>\n<p>Students often confuse <strong>Hamilton\u2019s canonical equations <\/strong>with <strong>Lagrange\u2019s equations<\/strong>, which is a fundamental mistake. Lagrange\u2019s equations, derived from the Lagrangian function, describe the motion of a system in terms of generalized coordinates and velocities. In contrast, Hamilton\u2019s canonical equations For CSIR NET describe the motion in terms of generalized coordinates and momenta, making it essential to understand Hamilton\u2019s canonical equations For CSIR NET. The distinction between these two sets of equations is crucial; it has significant implications for solving problems in classical mechanics.<\/p>\n<p>The key differences between the two sets of equations lie in their formulation and application. <strong>Lagrange\u2019s equations <\/strong>are<code>\\frac{d}{dt}(\\frac{\\partial L}{\\partial \\dot{q}_i}) - \\frac{\\partial L}{\\partial q_i} = 0<\/code>, where <em>L <\/em>is the Lagrangian, <em>q<sub>i <\/sub><\/em>are generalized coordinates, and<em>$\\dot{q}_i$ <\/em>are generalized velocities. On the other hand, <strong>Hamilton\u2019s canonical equations For CSIR NET <\/strong>are<code>\\dot{q}_i = \\frac{\\partial H}{\\partial p_i}<\/code>and<code>\\dot{p}_i = -\\frac{\\partial H}{\\partial q_i}<\/code>, where <em>H <\/em>is the Hamiltonian, <em>p<sub>i <\/sub><\/em>are generalized momenta, highlighting the importance of Hamilton\u2019s canonical equations For CSIR NET. Understanding these differences is necessary for success in CSIR NET, IIT JAM, and GATE exams.<\/p>\n<p>Understanding the distinction between these two sets of equations is <strong>necessary <\/strong>for success in CSIR NET, IIT JAM, and GATE exams, where Hamilton\u2019s canonical equations For CSIR NET are frequently tested. A thorough grasp of Hamilton\u2019s canonical equations For CSIR NET is essential for solving problems in classical mechanics.<\/p>\n<h2>Application: Hamilton\u2019s canonical equations For CSIR NET in Optics<\/h2>\n<p>Hamilton\u2019s canonical equations For CSIR NET have a <strong>specifically significant <\/strong>application in optics, particularly in the study of wave propagation. In optics, Hamilton\u2019s equations are used to derive the wave equation, which describes how light waves propagate through a medium. The wave equation is a fundamental equation in optics, and Hamilton\u2019s canonical equations For CSIR NET provide a powerful tool for deriving it, making Hamilton\u2019s canonical equations For CSIR NET essential for optics. This application is a significant area of study; it has numerous implications for the behavior of light.<\/p>\n<p>The wave equation can be derived from Hamilton\u2019s canonical equations For CSIR NET by considering the optical Hamiltonian, which is a function of the position and momentum of light rays. By applying Hamilton\u2019s equations to the optical Hamiltonian, researchers can obtain the wave equation, which is a partial differential equation that describes the propagation of light waves and demonstrates the application of Hamilton\u2019s canonical equations For CSIR NET. This derivation is a crucial step in understanding the behavior of light.<\/p>\n<p>These solutions have numerous applications in optics, including <em>optical communication systems<\/em>, <em>laser technology<\/em>, and <em>optical imaging<\/em>. For instance, Gaussian beams are widely used in laser technology due to their unique properties, such as high intensity and small beam waist, all of which rely on a deep understanding of Hamilton\u2019s canonical equations For CSIR NET. The study of Hamilton\u2019s canonical equations For CSIR NET has far-reaching implications for the field of optics.<\/p>\n<h2>Strategies for Solving Problems on Hamilton\u2019s canonical equations For CSIR NET<\/h2>\n<p>To tackle problems involving Hamilton\u2019s canonical equations in CSIR NET and IIT JAM, students should first focus on understanding the foundational concepts of Hamilton\u2019s canonical equations For CSIR NET. <strong>Hamilton\u2019s canonical equations For CSIR NET <\/strong>are a set of fundamental equations in classical mechanics that describe the time evolution of a physical system, making Hamilton\u2019s canonical equations For CSIR NET a <strong>critical area of study<\/strong>. A short sentence: Mastering Hamilton\u2019s canonical equations For CSIR NET requires practice.<\/p>\n<p>A key strategy for solving problems is to practice transforming <em>Lagrange\u2019s equations <\/em>into Hamilton\u2019s canonical equations For CSIR NET. Students should focus on <strong>key subtopics <\/strong>such as <em>Lagrange\u2019s equations<\/em>, the <em>principle of least action<\/em>, and the <em>Legendre transformation<\/em>, all of which are essential for mastering Hamilton\u2019s canonical equations For CSIR NET. The study of Hamilton\u2019s canonical equations For CSIR NET involves a deep understanding of these subtopics; it requires a systematic approach to learning.<\/p>\n<p>For effective preparation, students are advised to adopt a systematic study approach. This includes solving practice problems on Hamilton\u2019s canonical equations For CSIR NET, revising theoretical concepts, and referring to expert resources. <em><a href=\"https:\/\/www.vedprep.com\/\">VedPrep<\/a> <\/em>offers expert guidance and comprehensive study materials for CSIR NET, IIT JAM, and GATE, which can help students improve their understanding of Hamilton\u2019s canonical equations For CSIR NET. A long sentence: By adopting a systematic study approach, students can develop a deep understanding of Hamilton\u2019s canonical equations For CSIR NET, which is essential for success in competitive exams.<\/p>\n<p>Some frequently tested subtopics on Hamilton\u2019s canonical equations For CSIR NET include:<\/p>\n<ul>\n<li>Derivation of Hamilton\u2019s canonical equations For CSIR NET<\/li>\n<li>Applications of Hamilton\u2019s equations in classical mechanics and their relevance to Hamilton\u2019s canonical equations For CSIR NET<\/li>\n<li>Relationship between Lagrangian and Hamiltonian formulations and their connection to Hamilton\u2019s canonical equations For CSIR NET<\/li>\n<\/ul>\n<h2>Advanced Topics in Hamilton\u2019s canonical equations For CSIR NET<\/h2>\n<p>In relativistic mechanics, <strong>Hamilton&#8217;s equations <\/strong>play a <strong>pivotal <\/strong>role in describing the dynamics of particles, extending the applicability of Hamilton\u2019s canonical equations For CSIR NET. The relativistic <em>Hamiltonian <\/em>is defined as the total energy of the particle, which includes both kinetic and potential energy and is a key concept in Hamilton\u2019s canonical equations For CSIR NET. A short sentence: Relativistic mechanics is an advanced topic; it requires a deep understanding of Hamilton\u2019s canonical equations For CSIR NET.<\/p>\n<p>In <strong>quantum mechanics<\/strong>, Hamilton&#8217;s equations are used to describe the time-evolution of quantum systems, further highlighting the importance of Hamilton\u2019s canonical equations For CSIR NET. The <em>quantum Hamiltonian <\/em>is a self-adjoint operator that represents the total energy of the system, and the <code>von Neumann equation <\/code>is a quantum analogue of Hamilton&#8217;s equations, demonstrating the significance of Hamilton\u2019s canonical equations For CSIR NET. A long sentence: The application of Hamilton\u2019s canonical equations For CSIR NET to quantum mechanics is a significant area of study; it has far-reaching implications for our understanding of quantum systems.<\/p>\n<p>Hamilton&#8217;s canonical equations For CSIR NET have numerous applications in <strong>many-body systems <\/strong>and <strong>condensed matter physics<\/strong>. For example, they are used to study the behavior of <em>phonons <\/em>and <em>electrons <\/em>in solids, and to describe the <em>phase transitions <\/em>in magnetic systems, all of which rely on Hamilton\u2019s canonical equations For CSIR NET. A limitation of Hamilton\u2019s canonical equations For CSIR NET is that they assume a classical framework; they do not account for quantum effects.<\/p>\n<h2>Summary of Hamilton\u2019s canonical equations For CSIR NET<\/h2>\n<p>Hamilton\u2019s canonical equations For CSIR NET are a set of fundamental equations in classical mechanics that describe the time evolution of a physical system, making a thorough understanding of Hamilton\u2019s canonical equations For CSIR NET essential. These equations are derived from the Hamiltonian function, which is a mathematical representation of the total energy of the system and is central to Hamilton\u2019s canonical equations For CSIR NET. A short sentence: Hamilton\u2019s canonical equations For CSIR NET are widely used; they have numerous applications in physics.<\/p>\n<p>The Hamilton\u2019s canonical equations For CSIR NET are given by:<\/p>\n<ul>\n<li>$\\dot{q} = \\frac{\\partial H}{\\partial p}$<\/li>\n<li>$\\dot{p} = -\\frac{\\partial H}{\\partial q}$<\/li>\n<\/ul>\n<p>Understanding <strong>Hamilton\u2019s canonical equations For CSIR NET <\/strong>is <strong>critical <\/strong>for students preparing for competitive exams like CSIR NET, IIT JAM, and GATE, where Hamilton\u2019s canonical equations For CSIR NET play a vital role. These equations have numerous applications in physics, including the study of oscillations, rotations, and the behavior of complex systems, all of which rely on Hamilton\u2019s canonical equations For CSIR NET. A long sentence: The study of Hamilton\u2019s canonical equations For CSIR NET has far-reaching implications for our understanding of classical mechanics; it is an essential tool for physicists and engineers.<\/p>\n<section class=\"vedprep-faq\">\n<h2>Frequently Asked Questions<\/h2>\n<h3>Core Understanding<\/h3>\n<div class=\"faq-item\">\n<h4>What are Hamilton&#8217;s canonical equations?<\/h4>\n<p>Hamilton&#8217;s canonical equations are a set of 2n equations that describe the time evolution of a classical mechanical system. They are derived from the Hamiltonian function and are given by \u2202q\u1d62\/\u2202t = \u2202H\/\u2202p\u1d62 and \u2202p\u1d62\/\u2202t = -\u2202H\/\u2202q\u1d62.<\/p>\n<\/div>\n<div class=\"faq-item\">\n<h4>What is the Hamiltonian function?<\/h4>\n<p>The Hamiltonian function is a mathematical function that describes the total energy of a classical mechanical system. It is defined as the sum of the kinetic energy and potential energy of the system.<\/p>\n<\/div>\n<div class=\"faq-item\">\n<h4>What are the advantages of using Hamilton&#8217;s canonical equations?<\/h4>\n<p>The advantages of using Hamilton&#8217;s canonical equations include their ability to describe complex systems in a simple and elegant way, and their wide range of applications in physics and engineering.<\/p>\n<\/div>\n<div class=\"faq-item\">\n<h4>What are the limitations of Hamilton&#8217;s canonical equations?<\/h4>\n<p>The limitations of Hamilton&#8217;s canonical equations include their assumption of a conservative system and their inability to describe non-conservative systems.<\/p>\n<\/div>\n<div class=\"faq-item\">\n<h4>How are Hamilton&#8217;s canonical equations related to Lagrangian mechanics?<\/h4>\n<p>Hamilton&#8217;s canonical equations are related to Lagrangian mechanics through the Legendre transformation, which transforms the Lagrangian function into the Hamiltonian function.<\/p>\n<\/div>\n<div class=\"faq-item\">\n<h4>What is the relationship between Hamilton&#8217;s canonical equations and Poisson brackets?<\/h4>\n<p>Hamilton&#8217;s canonical equations can be expressed in terms of Poisson brackets, which provide a powerful tool for studying the properties of classical mechanical systems.<\/p>\n<\/div>\n<div class=\"faq-item\">\n<h4>What is the relationship between Hamilton&#8217;s canonical equations and symplectic geometry?<\/h4>\n<p>Hamilton&#8217;s canonical equations are closely related to symplectic geometry, which provides a powerful framework for studying the properties of classical mechanical systems.<\/p>\n<\/div>\n<div class=\"faq-item\">\n<h4>What is the relationship between Hamilton&#8217;s canonical equations and quantum mechanics?<\/h4>\n<p>Hamilton&#8217;s canonical equations have a close relationship with quantum mechanics, particularly in the study of quantum systems and the quantization of classical systems.<\/p>\n<\/div>\n<h3>Exam Application<\/h3>\n<div class=\"faq-item\">\n<h4>How are Hamilton&#8217;s canonical equations applied in CSIR NET?<\/h4>\n<p>Hamilton&#8217;s canonical equations are applied in CSIR NET to solve problems in classical mechanics, particularly in topics such as oscillations, rotations, and central force motion.<\/p>\n<\/div>\n<div class=\"faq-item\">\n<h4>What types of problems can be solved using Hamilton&#8217;s canonical equations in CSIR NET?<\/h4>\n<p>Problems that can be solved using Hamilton&#8217;s canonical equations in CSIR NET include finding the equation of motion, determining the stability of a system, and calculating the energy of a system.<\/p>\n<\/div>\n<div class=\"faq-item\">\n<h4>How can I use Hamilton&#8217;s canonical equations to solve problems in CSIR NET?<\/h4>\n<p>To use Hamilton&#8217;s canonical equations to solve problems in CSIR NET, first identify the Hamiltonian function, then derive the equations of motion, and finally solve the resulting differential equations.<\/p>\n<\/div>\n<div class=\"faq-item\">\n<h4>How can I use Hamilton&#8217;s canonical equations to solve problems in applied mathematics?<\/h4>\n<p>Hamilton&#8217;s canonical equations can be used to solve problems in applied mathematics, particularly in areas such as physics, engineering, and computer science, where classical mechanics plays a crucial role.<\/p>\n<\/div>\n<div class=\"faq-item\">\n<h4>How can I use Hamilton&#8217;s canonical equations to solve problems in classical mechanics?<\/h4>\n<p>Hamilton&#8217;s canonical equations can be used to solve problems in classical mechanics, particularly in topics such as oscillations, rotations, and central force motion.<\/p>\n<\/div>\n<h3>Common Mistakes<\/h3>\n<div class=\"faq-item\">\n<h4>What are common mistakes made when applying Hamilton&#8217;s canonical equations?<\/h4>\n<p>Common mistakes made when applying Hamilton&#8217;s canonical equations include incorrect identification of the Hamiltonian function, incorrect derivation of the equations of motion, and incorrect solution of the resulting differential equations.<\/p>\n<\/div>\n<div class=\"faq-item\">\n<h4>How can I avoid mistakes when applying Hamilton&#8217;s canonical equations?<\/h4>\n<p>To avoid mistakes when applying Hamilton&#8217;s canonical equations, carefully identify the Hamiltonian function, double-check the derivation of the equations of motion, and verify the solution of the resulting differential equations.<\/p>\n<\/div>\n<div class=\"faq-item\">\n<h4>What are some common misconceptions about Hamilton&#8217;s canonical equations?<\/h4>\n<p>Common misconceptions about Hamilton&#8217;s canonical equations include the idea that they are only applicable to simple systems, and that they are equivalent to Lagrangian mechanics.<\/p>\n<\/div>\n<div class=\"faq-item\">\n<h4>What are some common errors made when deriving Hamilton&#8217;s canonical equations?<\/h4>\n<p>Common errors made when deriving Hamilton&#8217;s canonical equations include incorrect application of the Legendre transformation, and incorrect calculation of the Hamiltonian function.<\/p>\n<\/div>\n<h3>Advanced Concepts<\/h3>\n<div class=\"faq-item\">\n<h4>What are some advanced applications of Hamilton&#8217;s canonical equations?<\/h4>\n<p>Advanced applications of Hamilton&#8217;s canonical equations include their use in quantum mechanics, quantum field theory, and symplectic geometry.<\/p>\n<\/div>\n<div class=\"faq-item\">\n<h4>How can I use Hamilton&#8217;s canonical equations to study complex systems?<\/h4>\n<p>To use Hamilton&#8217;s canonical equations to study complex systems, use techniques such as perturbation theory, stability analysis, and numerical methods to analyze the behavior of the system.<\/p>\n<\/div>\n<div class=\"faq-item\">\n<h4>How can I use Hamilton&#8217;s canonical equations to study integrable systems?<\/h4>\n<p>To use Hamilton&#8217;s canonical equations to study integrable systems, use techniques such as action-angle variables, adiabatic invariants, and soliton theory to analyze the behavior of the system.<\/p>\n<\/div>\n<div class=\"faq-item\">\n<h4>How can I use Hamilton&#8217;s canonical equations to study chaotic systems?<\/h4>\n<p>To use Hamilton&#8217;s canonical equations to study chaotic systems, use techniques such as Lyapunov exponents, fractal analysis, and numerical methods to analyze the behavior of the system.<\/p>\n<\/div>\n<\/section>\n<p>https:\/\/www.youtube.com\/watch?v=fr10BN7bK6g<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Hamilton&#8217;s canonical equations For CSIR NET are a set of equations in classical mechanics that describe the time evolution of a physical system. They are derived from the principle of least action and widely applied in mechanics, optics, and other fields.<\/p>\n","protected":false},"author":10,"featured_media":11168,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":"","rank_math_seo_score":84},"categories":[29],"tags":[2923,6241,6238,6239,6240,2922],"class_list":["post-11169","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-csir-net","tag-competitive-exams","tag-csir-net-classical-mechanics","tag-hamilton-s-canonical-equations-for-csir-net","tag-hamilton-s-canonical-equations-for-csir-net-notes","tag-hamilton-s-canonical-equations-for-csir-net-questions","tag-vedprep","entry","has-media"],"acf":[],"_links":{"self":[{"href":"https:\/\/www.vedprep.com\/exams\/wp-json\/wp\/v2\/posts\/11169","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.vedprep.com\/exams\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.vedprep.com\/exams\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.vedprep.com\/exams\/wp-json\/wp\/v2\/users\/10"}],"replies":[{"embeddable":true,"href":"https:\/\/www.vedprep.com\/exams\/wp-json\/wp\/v2\/comments?post=11169"}],"version-history":[{"count":3,"href":"https:\/\/www.vedprep.com\/exams\/wp-json\/wp\/v2\/posts\/11169\/revisions"}],"predecessor-version":[{"id":21474,"href":"https:\/\/www.vedprep.com\/exams\/wp-json\/wp\/v2\/posts\/11169\/revisions\/21474"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.vedprep.com\/exams\/wp-json\/wp\/v2\/media\/11168"}],"wp:attachment":[{"href":"https:\/\/www.vedprep.com\/exams\/wp-json\/wp\/v2\/media?parent=11169"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.vedprep.com\/exams\/wp-json\/wp\/v2\/categories?post=11169"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.vedprep.com\/exams\/wp-json\/wp\/v2\/tags?post=11169"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}